Question

x - 6y = -9\
-x + 7y = 12\
(\square, \square)

Explanation:

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

The two equations are:
\[

$$\begin{cases} x - 6y = -9 \\ -x + 7y = 12 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively:
\((x - 6y)+(-x + 7y)=-9 + 12\)
Simplify the left - hand side: \(x - 6y-x + 7y=y\), and the right - hand side: \(3\). So we get \(y = 3\).

Step2: Substitute \(y = 3\) into the first equation to find \(x\)

Substitute \(y = 3\) into the equation \(x-6y=-9\):
\(x-6\times3=-9\)
\(x - 18=-9\)
Add 18 to both sides of the equation: \(x=-9 + 18\)
\(x = 9\)

Answer:

\((9,3)\)