Question

solve the system of linear equations by elimination.
$x - 2y = -7$
$3x + 2y = 3$
solution: (\square, \square)

Explanation:

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

The system is:
\[

$$\begin{cases} x - 2y = -7 \\ 3x + 2y = 3 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((x - 2y)+(3x + 2y)=-7 + 3\)
Simplify the left - hand side: \(x-2y + 3x+2y=4x\), and the right - hand side: \(-7 + 3=-4\). So we get the equation \(4x=-4\)

Step2: Solve for \( x \)

Divide both sides of the equation \(4x=-4\) by 4:
\(x=\frac{-4}{4}=-1\)

Step3: Substitute \( x = - 1 \) into one of the original equations to solve for \( y \)

We substitute \( x=-1\) into the first equation \(x - 2y=-7\):
\(-1-2y=-7\)
Add 1 to both sides of the equation: \(-2y=-7 + 1=-6\)
Divide both sides by \(-2\): \(y=\frac{-6}{-2}=3\)

Answer:

\((-1,3)\)