Question

-4x + 2y = 30
4x + 2y = -10

Explanation:

Step1: Add the two equations

To eliminate \(x\), we add the two given equations: \((-4x + 2y)+(4x + 2y)=30+(-10)\)
Simplifying the left - hand side: \(-4x+4x + 2y+2y = 4y\)
Simplifying the right - hand side: \(30 - 10=20\)
So we get the equation \(4y = 20\)

Step2: Solve for \(y\)

Divide both sides of the equation \(4y = 20\) by 4: \(y=\frac{20}{4}=5\)

Step3: Substitute \(y = 5\) into one of the original equations

Let's substitute \(y = 5\) into the equation \(4x+2y=-10\)
We have \(4x+2\times5=-10\)
Simplify: \(4x + 10=-10\)

Step4: Solve for \(x\)

Subtract 10 from both sides: \(4x=-10 - 10=-20\)
Divide both sides by 4: \(x=\frac{-20}{4}=-5\)

Answer:

The solution to the system of equations is \(x = - 5\) and \(y = 5\)