Question

1. $-6x + 7y = 9$

$-6x - 6y = -30$

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}-6x + 7y = 9 \\ -6x - 6y = -30\end{cases}$$

Subtract the second equation from the first equation:
$$(-6x + 7y)-(-6x - 6y)=9-(-30)$$
Simplify the left side: $-6x + 7y + 6x + 6y = 13y$
Simplify the right side: $9 + 30 = 39$
So we get $13y=39$

Step2: Solve for y

Divide both sides of $13y = 39$ by 13:
$$y=\frac{39}{13}=3$$

Step3: Substitute y into one equation to solve for x

Substitute $y = 3$ into the first equation $-6x + 7y = 9$:
$$-6x+7\times3 = 9$$
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 to the system is $x = 2$ and $y = 3$.