Question

1. -5x - 7y = 7\\-4x - 2y = -16

Explanation:

Step1: Simplify the second equation

Divide the second equation \(-4x - 2y = -16\) by \(-2\) to get \(2x + y = 8\), then express \(y\) as \(y = 8 - 2x\).

Step2: Substitute \(y\) into the first equation

Substitute \(y = 8 - 2x\) into \(-5x - 7y = 7\):
\[

$$\begin{align*} -5x - 7(8 - 2x)&= 7\\ -5x - 56 + 14x&= 7\\ 9x - 56&= 7\\ 9x&= 7 + 56\\ 9x&= 63\\ x&= 7 \end{align*}$$

\]

Step3: Find the value of \(y\)

Substitute \(x = 7\) into \(y = 8 - 2x\):
\(y = 8 - 2\times7 = 8 - 14 = -6\)

Answer:

The solution to the system of equations is \(x = 7\) and \(y = -6\)