Question

solve the following system of equations.
-5x + 2y = 6
10x - 2y = -16

Explanation:

Step1: Add the two equations

Add the equations \(-5x + 2y = 6\) and \(10x - 2y = -16\) together.

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Step2: Solve for \(x\)

Divide both sides of the equation \(5x=-10\) by 5.

$$ x=\frac{-10}{5}=-2 $$

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

Substitute \(x=-2\) into the first equation \(-5x + 2y = 6\).

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Step4: Solve for \(y\)

Subtract 10 from both sides of the equation \(10 + 2y = 6\): \(2y=6 - 10=-4\). Then divide both sides by 2: \(y=\frac{-4}{2}=-2\).

Answer:

\(x = - 2\), \(y = - 2\)