Question

Solve each system by substitution. y=3x+4 y=4x+7

Answer 1

We need to solve the following system by substituition:

`\begin{cases}y=3x+4 \\ y=4x+7\end{cases}`

To solve by substituition means that we need to isolate one variable in one of the equations and replace one expression with the other. This is done below:

`\begin{gathered} (3x+4)=4x+7 \\ 3x+4=4x+7 \\ 3x-4x=7-4 \\ -x=3 \\ x=-3 \end{gathered}`

Then we need to replace the value of "x" in any of the two equations.

`\begin{gathered} y=3\cdot(-3)+4 \\ y=-9+4 \\ y=-5 \end{gathered}`

The solution is (-3,-5).