Question

Solve using elimination.2x - 3y = 1x + 3y = 17Show your work here:Solution:

Answer 1

Given

$\begin{gathered} 2x-3y=1\ldots Equation\text{ 1} \\ x+3y=17\ldots Equation\text{ 2} \end{gathered}$

Step 1

Add equation 1 and 2 to eliminate y:

$\begin{gathered} 2x+x-3y-3y=1+17 \\ 3x=18 \end{gathered}$

Divide both sides by 3

$\begin{gathered} \frac{3x}{3}=\frac{18}{3} \\ x=6 \end{gathered}$

Step 2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

$2x-3y=1$

Substitute for x=6

$\begin{gathered} 2(6)-3y=1 \\ 12-3y=1 \\ -3y=1-12 \\ -3y=-11 \\ \text{divide both sides by -3} \\ -\frac{3y}{-3}=-\frac{11}{-3} \\ y=\frac{11}{3} \end{gathered}$

The final answer

$\begin{gathered} x=6 \\ y=\frac{11}{3} \end{gathered}$