Question

Solve the system of equations: 2x + 3y = 8 and 3x - 3y = 12.

Answer 1

`(4,0)`

1) In this problem, let's solve this given system of equations by the method of Elimination.

We can start by adding both equations simultaneously:

`\begin{gathered} 2x+3y=8 \\ 3x-3y=12 \\ --------- \\ 5x=20 \\ \\ (5x)/(5)=(20)/(5) \\ \\ x=4 \end{gathered}`

Now, that we know the quantity of x, let's plug it into any of those equations. Most of the time, we opt to plug it into the simpler equation.

`\begin{gathered} 2x+3y=8 \\ 2(4)+3y=8 \\ 8+3y=8 \\ -8+8+3y=8-8 \\ 3y=0 \\ (3y)/(3)=(0)/(3) \\ \\ y=0 \end{gathered}`

2) Thus, the answer is (4,0)