Question

use elimination to solve the system of equations.
$x - y = 4$
$2x + y = -4$
$\left(\square,\square\
ight)$
need help?

Explanation:

Step1: Add the two equations to eliminate \( y \)

The system of equations is:
\[

$$\begin{cases} x - y = 4 \\ 2x + y = -4 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations: \((x - y)+(2x + y)=4+( - 4)\)
Simplify the left - hand side: \(x - y+2x + y=(x + 2x)+(y - y)=3x\)
Simplify the right - hand side: \(4+( - 4)=0\)
So we get the equation \(3x = 0\)

Step2: Solve for \( x \)

From \(3x = 0\), divide both sides by 3: \(x=\frac{0}{3}=0\)

Step3: Substitute \( x = 0 \) into one of the original equations to solve for \( y \)

We substitute \(x = 0\) into the first equation \(x - y = 4\)
We have \(0 - y = 4\), which can be rewritten as \(-y = 4\)
Multiply both sides by - 1: \(y=-4\)

Answer:

\((0, - 4)\)