Question

A system of linear equations is shown below.

2x + 4y = 10
3x – y = 8

Marla is attempting to prove that by replacing 2x + 4y = 10 with a different equation it will sometimes produce a new system of equations with the same solution. Marla plans on multiplying 2x + 4y = 10 by 2 and then adding the results to the equation 3x – y = 8 in order to create a new equation. Marla claims that the new equation that she will replace2x + 4y = 10with is7x + 7y = 12. Is Marla correct?

Answer 1

Answer:

No Marla is not correct

Step-by-step explanation:

Start with multiplying the equation 2x + 4y = 10 by 2 to get

2*(2x+4y) = 2*10

2*2x+2*4y = 2*10

4x+8y = 20

Now add this result to 3x - y = 8 and we end up with

(4x+8y) + (3x-y) = 20+8

(4x+3x) + (8y - y) = 20+8

7x + 7y = 28

We see that Marla is close but not entirely correct because the "12" in her answer should be "28" instead.