Question

1. -6x + 7y = 9

-6x - 6y = -30

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system:
\[

$$\begin{cases} -6x + 7y = 9 \quad (1)\\ -6x - 6y = -30 \quad (2) \end{cases}$$

\]
Subtract equation \((2)\) from equation \((1)\):
\[
(-6x + 7y) - (-6x - 6y) = 9 - (-30)
\]
Simplify the left - hand side: \(-6x + 7y + 6x + 6y=13y\)
Simplify the right - hand side: \(9 + 30 = 39\)
So we get the equation \(13y=39\)

Step2: Solve for \(y\)

Divide both sides of the equation \(13y = 39\) by \(13\):
\(y=\frac{39}{13}=3\)

Step3: Substitute \(y = 3\) into one of the original equations to solve for \(x\)

Substitute \(y = 3\) into equation \((1)\): \(-6x+7\times3 = 9\)
Simplify: \(-6x+21 = 9\)
Subtract \(21\) from both sides: \(-6x=9 - 21=-12\)
Divide both sides by \(-6\): \(x=\frac{-12}{-6}=2\)

Answer:

The solution of the system is \(x = 2\) and \(y=3\)