Question

solve using elimination.
10x - 5y = 5
-x + 2y = -14
(□, □)

Explanation:

Step1: Multiply the second equation

To eliminate \(x\), multiply the second equation \(-x + 2y=-14\) by \(10\).
\(10\times(-x + 2y)=10\times(-14)\)
\(-10x + 20y=-140\)

Step2: Add the two equations

Add the first equation \(10x - 5y = 5\) and the new second equation \(-10x + 20y=-140\).
\((10x-5y)+(-10x + 20y)=5+(-140)\)
\(10x-5y-10x + 20y=5 - 140\)
\(15y=-135\)

Step3: Solve for \(y\)

Divide both sides of \(15y=-135\) by \(15\).
\(y=\frac{-135}{15}=-9\)

Step4: Substitute \(y\) into an equation

Substitute \(y = - 9\) into the first equation \(10x-5y = 5\).
\(10x-5\times(-9)=5\)
\(10x + 45=5\)

Step5: Solve for \(x\)

Subtract \(45\) from both sides: \(10x=5 - 45=-40\)
Divide both sides by \(10\): \(x=\frac{-40}{10}=-4\)

Answer:

\((-4, -9)\)