Question

Use the linear combination method to solve the system of equations. *Explain each step of your solution.2x - 3y = 13x + 2y = 4

Answer 1

We have the next system of equations

`\begin{gathered} 2x-3y=13 \\ x+2y=4​ \end{gathered}`

We will multiply by -2 the second equation

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

Then we sum

`\begin{gathered} \text{ 2x-3y=13} \\ +-2x-4y=-8 \end{gathered}`

We simplify

`\begin{gathered} -7y=5 \\ y=-(5)/(7) \end{gathered}`

Then for x

`x=-2(-(5)/(7))+4`

Then we simplify

`x=(38)/(7)`

ANSWER

x=38/7

y=-5/7