Question

5x + 2y = -4
-2x - 2y = 4

Explanation:

Step1: Add the two equations

Add the equations \(5x + 2y = -4\) and \(-2x - 2y = 4\) together.
\[

$$\begin{align*} (5x + 2y)+(-2x - 2y)&=-4 + 4\\ 5x+2y-2x - 2y&=0\\ 3x&=0 \end{align*}$$

\]

Step2: Solve for \(x\)

Divide both sides of \(3x = 0\) by 3.
\[x=\frac{0}{3}=0\]

Step3: Substitute \(x = 0\) into one of the original equations

Substitute \(x = 0\) into the first equation \(5x+2y=-4\).
\[

$$\begin{align*} 5(0)+2y&=-4\\ 0 + 2y&=-4\\ 2y&=-4 \end{align*}$$

\]

Step4: Solve for \(y\)

Divide both sides of \(2y=-4\) by 2.
\[y=\frac{-4}{2}=-2\]

Answer:

The solution to the system of equations is \(x = 0\) and \(y=-2\)