Question

solve the system of equations using elimination: $-3x + 2y = 8$ and $-6x + 7y = -8$.

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), multiply the first equation \(-3x + 2y = 8\) by 2. We get:
\(2\times(-3x + 2y)=2\times8\)
\(-6x + 4y = 16\)

Step2: Subtract new equation from second

The second equation is \(-6x + 7y = -8\). Subtract \(-6x + 4y = 16\) from it:
\((-6x + 7y)-(-6x + 4y)=-8 - 16\)
Simplify: \(-6x + 7y + 6x - 4y=-24\)
\(3y=-24\)

Step3: Solve for \(y\)

Divide both sides by 3:
\(y=\frac{-24}{3}=-8\)

Step4: Substitute \(y\) into first equation

Substitute \(y = -8\) into \(-3x + 2y = 8\):
\(-3x + 2\times(-8)=8\)
\(-3x - 16 = 8\)

Step5: Solve for \(x\)

Add 16 to both sides: \(-3x=8 + 16=24\)
Divide by \(-3\): \(x=\frac{24}{-3}=-8\)

Answer:

\(x = -8\), \(y = -8\)