Question

solve using elimination. -8x + 5y = 14 8x - 10y = -4

Explanation:

Step1: Add the two equations

To eliminate \(x\), we add the equations \(-8x + 5y = 14\) and \(8x - 10y = -4\) together.
\((-8x + 5y)+(8x - 10y)=14+(-4)\)
Simplifying the left side: \(-8x + 8x+5y - 10y = - 5y\)
Simplifying the right side: \(14 - 4 = 10\)
So we get \(-5y=10\)

Step2: Solve for \(y\)

Divide both sides of \(-5y = 10\) by \(-5\):
\(y=\frac{10}{-5}=-2\)

Step3: Substitute \(y = - 2\) into one of the original equations

Let's substitute into the first equation \(-8x+5y = 14\).
Substitute \(y=-2\): \(-8x+5\times(-2)=14\)
Simplify: \(-8x - 10 = 14\)

Step4: Solve for \(x\)

Add 10 to both sides: \(-8x=14 + 10=24\)
Divide both sides by \(-8\): \(x=\frac{24}{-8}=-3\)

Answer:

\((-3, - 2)\)