Question

solve the system of linear equations by elimination.
$3x + 2y = 3$
$3x - 2y = -9$
solution: (\square, \square)

Explanation:

Step1: Eliminate y by adding equations

Add the two equations \(3x + 2y = 3\) and \(3x - 2y = -9\) together.
\((3x + 2y) + (3x - 2y) = 3 + (-9)\)
Simplify left side: \(3x + 3x + 2y - 2y = 6x\)
Simplify right side: \(3 - 9 = -6\)
So we get \(6x = -6\).

Step2: Solve for x

Divide both sides of \(6x = -6\) by 6.
\(x = \frac{-6}{6} = -1\).

Step3: Substitute x to find y

Substitute \(x = -1\) into the first equation \(3x + 2y = 3\).
\(3(-1) + 2y = 3\)
Simplify: \(-3 + 2y = 3\)
Add 3 to both sides: \(2y = 3 + 3 = 6\)
Divide by 2: \(y = \frac{6}{2} = 3\).

Answer:

\((-1, 3)\)