Question

Solve the System of Equations8x + 15y = -1174x + 9y=-75Write your answer as an ordered pair: (x,y)

Answer 1

We have to solve the system of linear equations:

`\begin{gathered} 8x+15y=-117 \\ 4x+9y=-75 \end{gathered}`

We can substract 2 times the second equation for the first equation and solve for y:

`\begin{gathered} (8x+15y)-2(4x+9y)=-117-2(-75) \\ 8x+15y-8x-18y=-117+150 \\ 0x-3y=33 \\ y=(33)/(-3) \\ y=-11 \end{gathered}`

Now, we can solve for x:

`\begin{gathered} 4x+9y=-75 \\ 4x+9(-11)=-75 \\ 4x-99=-75 \\ 4x=-75+99 \\ 4x=24 \\ x=(24)/(4) \\ x=6 \end{gathered}`

Answer: (x,y)=(6,-11)