Question

3x+y=-14x+3y=12use substitution to solve

Answer 1

We are given the following two equations

`\begin{gathered} 3x+y=-1\qquad eq.1 \\ 4x+3y=12\qquad eq.2 \end{gathered}`

We are asked to solve the equation using the substitution method.

Let us re-arrange the eq.1 for y and then substitute it into the eq.2

`\begin{gathered} 3x+y=-1 \\ y=-1-3x \end{gathered}`

Now substitute it into the eq.2

`\begin{gathered} 4x+3y=12 \\ 4x+3(-1-3x)=12 \\ 4x-3-9x=12 \\ -5x-3=12 \\ -5x=12+3 \\ -5x=15 \\ x=(15)/(-5) \\ x=-3 \end{gathered}`

Now substitute the value of x into the eq.1

`\begin{gathered} 3x+y=-1 \\ 3(-3)+y=-1 \\ -9+y=-1 \\ y=-1+9 \\ y=8 \end{gathered}`

Therefore, the solution of the given equations is (-3, 8)

x = -3

y = 8