Question

Arranging like terms; solve the linear system using elimination8x + 6y = -369y = -8x -66

Answer 1

Given the system of equations :

`\begin{gathered} 8x+6y=-36 \\ 9y=-8x-66 \end{gathered}`

arranging like terms

so,

`\begin{gathered} 8x+6y=-36 \\ 8x+9y=-66 \end{gathered}`

Subtract the first equation from the second equation :

`\begin{gathered} (8x+9y)-(8x+6y)=-66-(-36) \\ 8x+9y-8x-6y=-66+36 \\ (8x-8x)+(9y-6y)=-30 \\ 3y=-30 \\ \\ y=-(30)/(3)=-10 \end{gathered}`

Substitute with y at the first equation to find x

`\begin{gathered} 8x+6\cdot-10=-36 \\ 8x-60=-36 \\ 8x=60-36 \\ 8x=24 \\ \\ x=(24)/(8)=3 \end{gathered}`

So, the solution of the system is:

`\begin{gathered} x=3 \\ y=-10 \end{gathered}`