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} (3x)/(3)=(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} \\ -(3y)/(-3)=-(11)/(-3) \\ y=(11)/(3) \end{gathered}`

The final answer

`\begin{gathered} x=6 \\ y=(11)/(3) \end{gathered}`