Question

I need help solving the system equation algebraically using elimination :( !

Answer 1

`\text{ D) (8,-5)}`

Explanation:

Given the following system of equation.

`\begin{gathered} 4x+3y=17\text{ (1)} \\ 2x-3y=31\text{ (2)} \end{gathered}`

Using the elimination method, as a first step, multiply each equation by a suitable number so that the two equations have the same leading coefficient.

In this case, the equations have already the same coefficient -3 and 3, add the second equation from the first:

`4x+2x+3y+(-3y)=17+31`

Compute like terms and solve this new equation for x:

`\begin{gathered} 6x=48 \\ x=(48)/(6) \\ x=8 \end{gathered}`

Now, substitute x=8 into either equation (1) or (2) and solve for y:

`\begin{gathered} 4(8)+3y=17 \\ 32+3y=17 \\ 3y=-15 \\ y=-(15)/(3) \\ y=-5 \end{gathered}`