Question

I need to use substitution to solve each system of equations then, putting it into ordered pairs ( please ignore faded numbers under)

Answer 1

Given the system

$\begin{gathered} x+2y=13 \\ 3x-5y=6 \end{gathered}$

We clear x in the first equation

$\begin{gathered} x+2y-2y=13-2y \\ x=13-2y \end{gathered}$

And substitute in the second equation and simplify

$\begin{gathered} 3(13-2y)-5y=6 \\ 39-6y-5y=6 \\ 39-11y=6 \end{gathered}$

Solve for y

$\begin{gathered} 39-11y-39=6-39 \\ -11y=-33 \\ \frac{-11y}{-11}=\frac{-33}{-11} \\ y=3 \end{gathered}$

Next, substitute y = 3 in x

$x=13-2(3)=13-6=7$

Answer: ordered pairs is (7,3)