Question

The Substitution MethodSolve the following system of equations with the SUBSTITUTION METHOD.Write your answer as an Ordered Pair.If infinitely many solutions exist, enter 0 (00).If no solution exists, enter DNESystem of EquationsSolution5x + y = 1363 – 4y = 26

Answer 1

We want to solve the following system

$\begin{cases}5x+y=13 \\ 63-4y=26\end{cases}$

First, we're going to solve the second equation for one of the variables.

$\begin{gathered} 63-4y=26 \\ -4y=26-63 \\ -4y=-37 \\ y=\frac{37}{4} \end{gathered}$

Then, we're going to substitute (plug-in) this expression into the other equation and solve.

$\begin{gathered} 5x+(\frac{37}{4})=13 \\ 5x=13-\frac{37}{4} \\ 5x=\frac{52-37}{4} \\ 5x=\frac{15}{4} \\ x=\frac{3}{4} \end{gathered}$

And this is our solution.

$(\frac{3}{4},\frac{37}{4})$