Question

solve using elimination.
-8x - 5y = -14
-10x - 10y = 20
(□, □)

Explanation:

Step1: Simplify the second equation

Divide the second equation \(-10x - 10y = 20\) by \(-10\) to simplify.
\(\frac{-10x}{-10}-\frac{10y}{-10}=\frac{20}{-10}\)
\(x + y=-2\)
We can rewrite this as \(y=-x - 2\) or we can also multiply the first equation by 2 to make the coefficients of \(y\) suitable for elimination. Let's multiply the first equation \(-8x-5y=-14\) by 2:
\(2\times(-8x - 5y)=2\times(-14)\)
\(-16x-10y=-28\)

Step2: Eliminate \(y\)

Now we have two equations:

1. \(-16x-10y=-28\)
2. \(-10x - 10y=20\)

Subtract the second equation from the first equation:
\((-16x-10y)-(-10x - 10y)=-28 - 20\)
\(-16x-10y + 10x+10y=-48\)
Combine like terms:
\(-6x=-48\)

Step3: Solve for \(x\)

Divide both sides of \(-6x=-48\) by \(-6\):
\(x=\frac{-48}{-6}=8\)

Step4: Solve for \(y\)

Substitute \(x = 8\) into the simplified second equation \(x + y=-2\):
\(8 + y=-2\)
Subtract 8 from both sides:
\(y=-2 - 8=-10\)

Answer:

\((8, - 10)\)