Question

Solve the system with elimination.3x + y = 9x + 2y = 3

Answer 1

In order to solve by elimination, let's multiply the first equation by -2. This way, when we add the equations, the variable y will be canceled out:

$\begin{cases}-6x-2y=-18 \\ x+2y={3}\end{cases}$

Now, adding the equations, we have:

$\begin{gathered} -6x-2y+x+2y=-18+3\\ \\ -5x=-15\\ \\ x=\frac{-15}{-5}\\ \\ x=3 \end{gathered}$

Now, calculating the value of y, we have:

$\begin{gathered} x+2y=3\\ \\ 3+2y=3\\ \\ 2y=0\\ \\ y=0 \end{gathered}$

Therefore the solution is (3, 0).