Question

Find an equivalent system of equations for the following system:

x + 2y = 2
- 4x + 4y = -8
x + 2y = 2
- 4x - 2y = 10
x + 2y = 2
5x + 4y = 8
x + 2y = 2
5x - 2y = 10
x + 2y = 2
5x – 2y = -8

Answer 1

x + 2y = 2 and 5x − 2y = 10

Explanation:

I took the test and got it right.

Answer 2

`\left\{\begin{array}{l}x+2y=2\\ \\5x-2y=10\end{array}\right.`

Explanation:

Given the system of equations

`\left\{\begin{array}{l}x+2y=2\\ \\-4x+4y=-8\end{array}\right.`

Subtract from the first equation the second equation:

`x+2y-(-4x+4y)=2-(-8)\\ \\x+2y+4x-4y=2+8\\ \\(x+4x)+(2y-4y)=10\\ \\5x-2y=10`

Therefore, equivalent system is

`\left\{\begin{array}{l}x+2y=2\\ \\5x-2y=10\end{array}\right.`