Question

solve using elimination.
$4x + 9y = -7$
$-2x - 9y = -1$

Explanation:

Step1: Eliminate y by adding equations

Add the two equations \(4x + 9y = -7\) and \(-2x - 9y = -1\) together.
\((4x + 9y)+(-2x - 9y)=-7+(-1)\)
Simplify left side: \(4x - 2x+9y - 9y = 2x\)
Simplify right side: \(-7 - 1=-8\)
So we get \(2x=-8\)

Step2: Solve for x

Divide both sides of \(2x = -8\) by 2.
\(x=\frac{-8}{2}=-4\)

Step3: Substitute x to find y

Substitute \(x = -4\) into the first equation \(4x + 9y=-7\).
\(4\times(-4)+9y=-7\)
Calculate \(4\times(-4)=-16\), so \(-16 + 9y=-7\)
Add 16 to both sides: \(9y=-7 + 16 = 9\)
Divide by 9: \(y=\frac{9}{9}=1\)

Answer:

\((-4, 1)\)