Question

solve the following system of equations.
2x - 5y = 4
-2x + 10y = -14

Explanation:

Step1: Add the two equations

Add the equations \(2x - 5y = 4\) and \(-2x + 10y = -14\) together.
\((2x - 5y)+(-2x + 10y)=4+(-14)\)
Simplify the left side: \(2x - 2x- 5y + 10y = 5y\)
Simplify the right side: \(4 - 14=-10\)
So we get \(5y=-10\)

Step2: Solve for y

Divide both sides of \(5y = - 10\) by 5.
\(y=\frac{-10}{5}=-2\)

Step3: Substitute y into the first equation

Substitute \(y = - 2\) into \(2x-5y = 4\).
\(2x-5\times(-2)=4\)
Simplify: \(2x + 10 = 4\)

Step4: Solve for x

Subtract 10 from both sides: \(2x=4 - 10=-6\)
Divide both sides by 2: \(x=\frac{-6}{2}=-3\)

Answer:

\(x = - 3\), \(y=-2\)