Question

Solve this system of equations usingthe substitution method.y = x + 9y = -4x – 612] [UN

Answer 1

The given system of equations is

`\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}`

We will substitute y in equation (2) by equation (1)

`x+9=-4x-6`

Now, add 4x to both sides

`\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}`

Subtract 9 from both sides

`\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}`

Divide both sides by 5

`\begin{gathered} (5x)/(5)=(-15)/(5) \\ x=-3 \end{gathered}`

Substitute x by -3 in equation (1) to find y

`\begin{gathered} y=-3+9 \\ y=6 \end{gathered}`

The solution of the system is (-3, 6)