Chapter 9.7, Problem 4GP

To determine

To solve : the given system of equations.

Answer to Problem 4GP

The solution of the given system of equations is $\text{(6},6)$ .

Explanation of Solution

Given information :

The given system of equations:

  $\begin{array}{l}\text{3}x+2y=30\\ x-2y=-6\end{array}$

Calculation :

As per problem,

Consider the system of equations:

  $\begin{array}{l}\text{3}x+2y=30\\ x-2y=-6\end{array}$

Solve the second equation for $x$ since its coefficient is $1$ .

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}\text{}x-2y=-6\text{ [Write the second equation]}\\ x-2y+2y=-6+2y\text{ [Add 2}y\text{ to each side]}\\ x=2y-6\text{ [Simplify}]\end{array}$

Find the value of $y$ by substituting $2y-6$ for $x$ in the first equation.

  $\begin{array}{l}\text{ 3}x+2y=30\text{ [Write the first equation]}\\ \text{3(}2y-6)+2y=30\text{ [Substitute }x=2y-6\text{]}\\ \text{ 6}y-18+2y=30\text{ [Distributive property}]\\ 8y-18=30\text{ [Combine like terms}]\\ 8y-18+18=30+18\text{ [Add 18 to each side}]\\ 8y=48\text{ [Simplify}]\\ \frac{8y}{8}=\frac{48}{8}\text{ [Divide both sides by }8]\\ y=6\text{ [Simplify}]\end{array}$

Substitute $6$ for $y$ in either equation to find the value of $x$ .

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}\text{}x-2y=-6\text{ [Write the second equation]}\\ x-2(6)=-6\text{ [}y=6\text{]}\\ x-12=-6\text{ [Simplify}]\\ x=6\text{ [Add 12 to each side}]\end{array}$

The solution of this system of equations is $\text{(6},6)$ .