Question

$y = 2x + 2 \\ y = 7x + 11$how do you solve this equation with substitution?

Answer 1

$x=-\frac{9}{5},y=-\frac{8}{5}$

1) As the chosen method to solve this Linear System of equations then we can write out the following:

$\mleft\{\begin{matrix}y=2x+2 \\ y=7x+11\end{matrix}\mright.$

2)Let's start with the simplest equation between them. And then, plug into that the value of "y". This way:

$\begin{gathered} \mleft\{\begin{matrix}I)y=2x+2 \\ II)y=7x+11\end{matrix}\mright. \\ I)y=2x+2 \\ 7x+11=2x+2 \\ 7x+11-2x=2x-2x+2 \\ 5x+11=2 \\ 5x+11-11=2-11 \\ 5x=-9 \\ \frac{5x}{5}=-\frac{9}{5} \\ x=-\frac{9}{5} \end{gathered}$

Now, that we know the quantity of "x", let's plug it into any one of those equations.

3)Let's pick the 2nd one and solve it for "y".

$\begin{gathered} y=7x+11,x=-\frac{9}{5} \\ y=7(-\frac{9}{5})+11 \\ y=-\frac{63}{5}+11 \\ y=-\frac{63}{5}+\frac{55}{5} \\ y=-\frac{8}{5} \end{gathered}$

Thus, the answer is:

$x=-\frac{9}{5},y=-\frac{8}{5}$