Question

Use elimination to solve for the values of x and y, written as the ordered pair (x, y). A. (3, 2)B. (-3, -2)C. (2, 3)D. (-2, -3)

Answer 1

Given the system of equations:

$\begin{cases}x+y=5 \\ 8x+4y=28\end{cases}$

We will use the elimination method to solve the system of equations

To eliminate (y), multiply the first equation by (-4) which is the opposite of the coefficient of (y) for the second equation

$\begin{gathered} \begin{cases}x+y=4\rightarrow\times-4 \\ 8x+4y=28\end{cases} \\ ============ \\ \begin{cases}-4x-4y=-20 \\ 8x+4y=28\end{cases} \\ \end{gathered}$

Add the equations, note (y) will be eliminated

$\begin{gathered} -4x+8x=-20+28 \\ 4x=8 \\ x=\frac{8}{4}=2 \end{gathered}$

Substitute with (x) into the first equation to find (y)

$\begin{gathered} 2+y=5 \\ y=5-2 \\ y=3 \end{gathered}$

So, the solution to the system is the point (2, 3)

The answer will be option C. (2, 3)