Chapter 9.2, Problem 18WE

To determine

To find: Thesolution of the given equations by using substitution method.

Answer to Problem 18WE

The solution of the given equations by using substitution method is $y=-4\text{and }x=-3$ .

Explanation of Solution

Given information:

The given equationsare,

  $\begin{array}{l}\frac{y}{2}-x=1\\ x+y+7=0\end{array}$

The given equation can be writtenas,

  $\begin{array}{l}x+y+7=0\\ x=-y-7\end{array}$

The another given equation is,

  $\frac{y}{2}-x=1$

Substitute $-y-7$ for $x$ .

  $\begin{array}{l}\frac{y}{2}-\left(-y-7\right)=1\\ \frac{3y}{2}+7=1\\ \frac{3y}{2}=-6\\ y=-4\end{array}$

The value of $x$ is calculated as,

  $\begin{array}{c}x=-y-7\\ =-\left(-4\right)-7\\ =-3\end{array}$

Thus, the solution of the given equations by using substitution method is $y=-4\text{and }x=-3$ .