1.  Lisa is working with the system of equations x + 2y = 7 and 2x ‒ 5y = 5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y = 9, telling her that y = 1. Lisa then finds that x = 5. Thinking about this procedure, Lisa wonders:
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by ‒2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?

What is the answer to Lisa’s question? Explain.

2.  Does the answer to the first question change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?

Answers

Answer 1
All methods are supposed to be correct in most if not all situations and it should not matter if you use a different method given the options
Answer 2

Answer:

1. Yes

2. Yes

Step-by-step explanation:

1. Lets test Lisa's different solution. Lets times 5 to the first equation:

[tex]5\cdot{x}+10\cdot{y}=35[/tex]

and 2 times the second equation:

[tex]4\cdot{x}-10\cdot{y}=10[/tex]

lets add the two equations:

[tex]9\cdot{x}=45[/tex]

[tex]x=5[/tex]

The second method is multiplying the first equation by -2:

[tex]-2\cdot{x}-4\cdot{y}=-14[/tex]

and add the second equation:

[tex]-9\cdot{y}=-9[/tex]

[tex]y=1[tex]

Substitute into equation 1:

[tex]x+2\cdot{1}=7[/tex]

[tex]x=5[/tex]

The answer to Lisa's question is yes she wull get the same solution if she uses a different method.

2. Yes, The answer would change if the same amout of x and y values are the same and therefore we cannot solve for x and y. If there was infinitely many solutions we would have quadratic equations.


Related Questions

Almost done. Math has been my worst nightmare since 6th grade.

Answers

If you are say are you right then yes you are right
Same here. i hate math. can't help with problem sorry. try using google.

Assume that 300300 births are randomly selected and 144144 of the births are girls. use subjective judgment to describe the number of girls as significantly​ high, significantly​ low, or neither significantly low nor significantly high.

Answers

The number of girls would neither be significantly high or low. Going off the conventional wisdom that holds that 51% of the population of the world is female, this would mean that 153 females would be born in 300 people, irrespective of viability rate. A random selection of 300 births leading to 144 girls would only be 3% outside the mean value, so this is not a significant difference.

Which equation is related to this equation? b + 17 = 52
a. b = 52 + 17
b. b = 52 ∙ 17
c. b = 52 ÷ 17
d. b = 52 – 17 question resources?

Answers

b+17=52 b=35
b=52-17
52-17=35

help please with b. and d.

Answers

I'm assuming the question is asking for you to factor the expressions.

b.
(x-3)(x+2)
-3+2=-1
-3*2=-6

d.
(x-6)(x-7)
-6-7=-13
-6*-7=42

The sum of the digits of a two-digit number is 6. when the digits are reversed, the number decreased by 18. find the original number.

Answers

2x + x = 12
=> x =12/3 =4
so, original number is 84.

A paint store sells exterior paint for $28.25 a gallon and paint rollers for $6.25 each. Write an equation in standard form for the number of gallons p of paint and rollers r that a customer could buy with $145.

Answers

28.25p + 6.25r = 145 <== ur equation

Which conditional statement is false?
A. If a figure has four congruent angles, then it is a square.
B. If two figures are congruent, then they have equal perimeters.
C. If two figures are congruent, then they have equal side and angle measurements.

Answers

Statement A. If a figure has four congruent angles, then it is a square is false. For one, a rectangle serves as a counterexample having four congruent angles but it is not a square.

The statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).

What is the conditional statement?

A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).

Let us consider the example to understand the parts of a conditional statement.

Conditional Statement: If today is Friday, then yesterday was Thursday.

Hypothesis: "If today is Friday."

In the given problem,

Conditional Statement:  If a figure has four congruent angles, then it is a square

Hypothesis: "If a figure has four congruent angles"

One example of a counterexample is a rectangle, which although not a square, has four congruent angles.

Hence, the statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).

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A 12 ft rope cut into two pieces so that one piece is 3 ft less than twice the length if the other piece. How long is each piece?

Answers

the answer is 9 feet because 9+3 is 12 and something twice is multiply.3x3 would be 9 making that the twice part......i think lol

Solve for x. 5.6x = 39.76

Answers

5.6x = 39.76
divide both side by 5.6
5.6x/5.6 = 39.76 / 5.6
simply 
x = 7.1
5.6x = 39.76

Divide 39.76 by 5.6

Answer = x = 7.1

Does there exist a function that is not a relation

Answers

No, a function is always a relation. A relation may not always a function but the vice versa is true.

It's like the relationship between a rectangle and a square. A rectangle has 4 right angles and 2 sets of congruent sides while a square has 4 right angles and all sides are congruent. Which means that a rectangle is a square, but a square may not always be a rectangle.
Final answer:

Every function is a kind of relation by definition. A function is a relation where every input is paired with exactly one output. Therefore, there doesn't exist a function that isn't a relation.

Explanation:

In mathematics, every function is a relation, but not every relation is a function. A function is a special type of relation where every input (or x-value) is paired with exactly one output (or y-value). This is often referred to as the vertical line test. If any vertical line intersect the graph of the relation at more than one point, then it is not a function. Therefore, there does not exist a function that is not a relation, because by definition, a function is always a relation.

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(01.05) what is the slope-intercept form equation of the line that passes through (3, 4) and (5, 16)? (1 point) y = 6x − 14 y = −6x + 14 y = −6x − 14 y = 6x + 14

Answers

(3,4)(5,16)
slope = (16 - 4) / (5 - 3) = 12/2 = 6

y = mx + b
slope(m) = 6
use either of ur points (3,4)...x = 3 and y = 4
sub and find b, the y int
4 = 6(3) + b
4 = 18 + b
4 - 18 = b
-14 = b

so ur equation is : y = 6x - 14

Answer:

The answer is [tex]y=6x-14[/tex]

Step-by-step explanation:

In order to determine the slope-intercept form equation, we need to know the formula. The formula needs a slope (m) and a point (x,y) that belongs to the equation.

[tex]y-y_1=m(x-x_1)\\m=slope\\(x_1,y_1)=point[/tex]

For m:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, first we have to define every variable and then we replace them into the formula:

[tex]P_1=(3,4)\\P_2=(5,16)\\m=\frac{16-4}{5-3}\\m=\frac{12}{2}=6[/tex]

It doesn't matter the order of how you define the points. The result will be the same.

Then:

[tex]y-4=6*(x-3)\\y=6*(x-3)+4\\y=6x-18+4\\y=6x-14[/tex]

Finally, the slope-intercept form equation is [tex]y=6x-14[/tex]

Fat harry got on the scale at 7:00
a.m. and weighed 295 pounds. at 7:02
a.m. he again got on the scale and weighed 200 pounds. at 7:04 he weighed 499 pounds. the measurement of harry's weight has problems with

Answers

I would say it has major problems with the weighing scales!!

Answer:

Harry's weight fluctuated significantly within minutes, indicating a potential issue with the scale's accuracy or calibration. He should address the problem to ensure reliable weight measurements.

Explanation:

It seems like there might be a problem with the scale's accuracy or consistency. Harry's weight fluctuated significantly within just a few minutes, which is highly unlikely under normal circumstances. Such drastic changes in weight in such a short amount of time are not physically possible, indicating a potential issue with the scale's functionality or calibration. It's possible that the scale is malfunctioning, providing inaccurate readings, or there may be external factors affecting the measurements, such as an unstable surface or improper usage of the scale. It's important for Harry to address this issue with the scale and possibly seek assistance from a professional to ensure accurate and reliable weight measurements.

Find three consecutive odd integers such that the sum of the first, two time the second and three times the third is 46

Answers

5+(2*7)+(3*9) = 46


I'm  assuming this is what you meant.

To find the three consecutive odd integers that satisfy the given conditions, we set up an equation x + 2(x + 2) + 3(x + 4) = 46, solved it to find x = 5, and then found the integers as 5, 7, and 9.

We are given a problem to find three consecutive odd integers where the sum of the first, two times the second, and three times the third equals 46. Let's label our integers as x (the first), x+2 (the second), and x+4 (the third), as the differences between odd integers are 2.

The equation, based on the problem statement, is:
x + 2(x + 2) + 3(x + 4) = 46

Distribute and combine like terms:
x + 2x + 4 + 3x + 12 = 46
6x + 16 = 46

Subtract 16 from both sides:
6x = 30
Divide both sides by 6:
x = 5

Therefore, the three consecutive odd integers are:
x = 5 (first integer),
x + 2 = 7 (second integer),
x + 4 = 9 (third integer).

Checking the solution: 5 + 2(7) + 3(9) = 5 + 14 + 27 = 46, which confirms our answer is correct.

Find the eleventh term of the last term of A.P.
27,23,19,.....-65.

Answers

The term to term rule is to subtract 4

Term 1 = 27
Term 2 = 27 - 4 = 23
Term 3 = 23 - 4 = 19
Term 4 = 19 - 4 = 15
Term 5 = 15 - 4 = 11
Term 6 = 11 - 4 = 9
Term 7 = 9 - 4 = 5
Term 8 = 5 - 4 = 1
Term 9 = 1 - 4 = -3
Term 10 = -3 - 4 = -7
Term 11 = -7 - 4 = -11

The eleventh term = -11

Amy is a software saleswoman. Her base salary is 2300, and she makes and an additional $80 for every copy of English is fun she sells. Let p represent her total pay ( in dollars ), and let N represent the number of copies of English is fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 21 copies of English is fun

Answers

S = 2100 + 40N Think of the graph as your typical (X,Y) graph but with the axis being (N,S) instead.  

Convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar 5/frac{7}{10}

Answers

[tex]5 \frac{7}{10}= \frac{5*10+7}{10}= \frac{57}{10} [/tex]

Answer is 57/10

Prove that if you pick three socks from a from a drawer containing only black or blue socks that you must get a pair or either black or blue.

Answers

All you have to do is pick them up if you only got two color and u pic up three that means u got two of the same color and one different color.

Larry has $20 to spend at the store. He plans to purchase five items that cost $5.79, $7.63, $3.46, $2.99, and $3.65. Larry estimated his total cost to make sure he has enough money for his purchases. Is his estimate accurate? Explain why or why not. $5 + $7 + $3 + $2 + $3 = $20

Answers

Answer:

Larry did not round correctly. He used front-end estimation, but he did not round up when appropriate. His estimate will be lower than the amount of money he needs.

Step-by-step explanation:

yeah

Larry's estimation is incorrect.

The total cost of the items that Larry bought will be:

= $5.79 + $7.63 + $3.46 + $2.99 + $3.65

= $23.65

Since Larry estimated his total cost to be $20 while the correct answer is $23.65, then his estimate is wrong.

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Given below is the odd-number function. Which of the following are equal to O(9)? Check all that apply.

O(n) = 2n - 1

A. The ninth odd number

B. O(8) + 2

C. 9

D. 17

Answers

The correct answers will be A. The ninth odd number. B.O(8) + 2 and D.17.

I did this too and those were the right answers!

I hope this helps! :>

simplify -52 + 8|-1| + (-3)

Answers

Answer is -47

First take the 8|-1|
anything between the lines is turned positive. therefore it simplifys to just 8 * 1 
so now we have -52 + 8 + (-3)
-52 + 8= -44
-44+(-3)=-47
| -1| = 1 (absolute value always make it positive)

therefore

8 x 1 = 8

-52 - 3 = -55

-55 + 8 = -47

-47 is your answer

hope this helps

Death Valley, California has the lowest elevation in the United States. It's elevation is 282 feet below sea level. Mount McKinley Alaska has the highest elevation in the United States. It's elevation is 20,320 feet above sea level. Use integers to describe these two locations in the United States.

Answers

Answers:

1)  -282 .

2)  20,320 .
_______________________

Answer:

Death Valley's elevation is -282 feet and Mount McKinley Alaska elevation is 20,320 feet

Step-by-step explanation:

Consider the provided information.

Integers are the number that do not contain any decimal or fraction. They contains positive counting number, negative counting numbers and zero.

For example:{...-3,-2,-1,0,1,2,3...}

It is given that Death Valley, California has the lowest elevation in the United States. It's elevation is 282 feet below sea level.

Mount McKinley Alaska has the highest elevation in the United States. It's elevation is 20,320 feet above sea level.

We need to use integers to describe these two locations in the United States.

Both the statements are related with sea level.

Let say the sea level is at the zero, if a point is below sea level then we will indicate it by placing a negative sign in the front of the number and if it is above the sea level then we will indicate it by placing a positive sign or no sign in the front of the number.

Now consider the provided information.

Death Valley's elevation is 282 feet below sea level.

Which can be written as: -282 Feet (In integer)

Mount McKinley Alaska elevation is 20,320 feet above sea level.

Which can be written as: 20,320 Feet (In integer)

1.5d + 3.25 = 1 + 2.25d ---What are the steps to find x?

Answers

Do u mean d?

1.5d +3.25 = 1 +2.25d  
3.25 = 1 + .75d              -1.5d on both sides
2.25 = .75d                      subtraction 1 on both sides
3 = d                                  divide both sides by .75
 

Write the standard equation of the line that passes through the point (-1,12) and has the same slope as a vertical line

Answers

Vertical lines have undefined slope. They are not y=mx+b equations, but simply x= equations.

This line passes through the point (-1,12) has an x-value of -1. Therefore the equation of the line is simply  x=-1

1/6 ÷4/7=?please help I don't understand this

Answers

To divide fractions, we multiply the forst numberby the reciprocal of the second.
Reciprocal of 4/7= 7/4

1/6*7/4= 7/24

Final answer: 7/24

Jacob can run a 6 minute mile. If he runs at that pace for 25 minutes,how many miles can Jacob run?

Answers

Your Answer Is...

3 1/6.

Glad I Could Help, And Good Luck!

A builder could get 6 sheets of shreetrock for 9$ if he bought 12 sheets, how much money would we have spent

Answers

12/6 = 2
9x2= 18

A builder would spent 18$
Final answer:

With the given ratio of $9 for 6 sheets of sheetrock, the builder would spend $18 if he bought 12 sheets of sheetrock.

Explanation:

This is a question about simple ratios in mathematics. In the given situation, the ratio of the price is $9 for 6 sheets of sheetrock. To calculate the cost of 12 sheets, we simply need to multiply the price for 6 sheets by 2.

Alternatively, you could set up a proportion to solve this problem: 9 dollars / 6 sheets = x dollars / 12 sheets. After solving for x, we get x = 18 dollars.

So, if the builder bought 12 sheets of sheetrock, he would have spent $18.

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Find k so that the three equations 3x-y=2, 2x+8=3y, and y=kx have a common solution

Answers

2x+8=3kx (3k-2)x+8=0
3x-kx=2. (3-k)x-2=0
3k-2)x+10=3-k)x
4k-5=10/x
///////
3x-y-2=2x+8-3y
X+2y-10=0
X+2kx-10=0
K=(10-x)/2x

Jack leaves the caves and runs directly north for 9 miles. He then turns and runs 12 miles east. How many miles is he from the caves?

Answers

a^2 + b^2 = c^2
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
sqrt 225 = c
15 = c <=== Jack is 15 miles from the cave
it is 9 miles or 21 miles but i think it is 9 miles

A small plane traveled from city a to city​ b, averaging 169169 miles per hour. the trip took twotwo hours. what is the distance from city a to city​ b?

Answers

1409.7 miles from city a to city b

If you know the pythagorean theorem, then you can always find the distance between two points in the plane.

Answers

the answer to this question is true

Answer:

The Answer Is True

Step-by-step explanation:


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