Chapter 6.2, Problem 12PPE

To determine

To solve: The system of linear equations using substitution.

Answer to Problem 12PPE

The solution is x = 8 and y = 11.

Explanation of Solution

Given information:

The equations $y=x+3$ and $2x+2y=38$

Calculation:

Substitute $x+3$ for y in equation $2x+2y=38$

  $2x+2\left(x+3\right)=38$

Now simplify above equation.

  $\begin{array}{l}2x+2\left(x+3\right)=38\\ \Rightarrow 2x+2x+6=38\\ \Rightarrow 4x+6=38\\ \Rightarrow 4x=32\\ \Rightarrow x=8\end{array}$

Use above value of in equation $y=x+3$

  $y=8+3=11$

Therefore the solution is x = 8 and y = 11.

Check

  $\begin{array}{l}y=x+32x+2y=38\\ 11=8+32\left(8\right)+2\left(11\right)=38\\ 11=1116+22=38\\ 38=38\end{array}$