Question

X + y = -5(x- y=9 Solve by elimination

Answer 1

(x, y) = (2, -7)

Explanation:

Given the system of equations:

`\begin{cases}x+y=-5 \\ x-y=9\end{cases}`

We are required to solve the system by the elimination method.

In order to do this, add the two equations.

`\begin{gathered} \begin{cases}x+y=-5 \\ x-y=9\end{cases} \\ --------- \\ 2x=4 \end{gathered}`

Divide both sides by 2 to solve for x.

`\begin{gathered} (2x)/(2)=(4)/(2) \\ x=2 \end{gathered}`

Next, substitute x=2 into any of the equations to solve for y.

Using the first equation:

`\begin{gathered} x+y=-5 \\ 2+y=-5 \\ y=-5-2 \\ y=-7 \end{gathered}`

The solution to the system of linear equations is (x, y) = (2, -7).