Michiko claims that to solve the system of linear equations 15x+8y=1 and 21x+4y=-13, instead of multiplying the second equation by - 2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct?

A Michiko is right for this system of linear equations, but her method will not

work for other systems of linear equations.

B Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.

C Michiko is wrong because her method will give the opposite of the correct value for x for any system of linear equations.

D Michiko is wrong because her method will give the opposite of the correct value for y for any system of linear equations.

Question

Moises

Mathematics

20 March, 11:39

Michiko claims that to solve the system of linear equations 15x+8y=1 and 21x+4y=-13, instead of multiplying the second equation by - 2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct?

A Michiko is right for this system of linear equations, but her method will not

work for other systems of linear equations.

B Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.

C Michiko is wrong because her method will give the opposite of the correct value for x for any system of linear equations.

D Michiko is wrong because her method will give the opposite of the correct value for y for any system of linear equations.

+3

Answers (1)

Know the Answer?

Tamia Schmitt · Answer 1

For this case we have the following equations:

15x + 8y = 1

21x + 4y = - 13

We can rewrite the system as:

15x + 8y = 1

-42x-8y = 26

Or equivalently:

15x + 8y = 1

42x + 8y = - 26

Next we have:

Method 1:

Add equations:

-27x = 27

Method 2:

Subtract equations:

-27x = 27

Therefore, both methods work correctly.

Answer:

B Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.