Question

solve using elimination.
x - 5y = -19
10x - 8y = 20

Explanation:

Step1: Multiply first equation by 10

To eliminate \(x\), multiply the first equation \(x - 5y=-19\) by 10. We get \(10x-50y = - 190\).

Step2: Subtract the two equations

Now we have two equations:
\(10x - 50y=-190\) (from step 1)
\(10x - 8y = 20\) (given)

Subtract the second equation from the first: \((10x-50y)-(10x - 8y)=-190 - 20\)
Simplify: \(10x-50y - 10x + 8y=-210\)
\(-42y=-210\)

Step3: Solve for y

Divide both sides by \(- 42\): \(y=\frac{-210}{-42}=5\)

Step4: Substitute y into first equation

Substitute \(y = 5\) into \(x-5y=-19\): \(x-5\times5=-19\)
\(x - 25=-19\)

Step5: Solve for x

Add 25 to both sides: \(x=-19 + 25=6\)

Answer:

\((6,5)\)