Chapter 9.7, Problem 28STP

To determine

To choose : the correct answerfor $-2y$ .

Answer to Problem 28STP

Option J. $-6$ is the correct value of $-2y$ .

Explanation of Solution

Given information :

The given system of equations:

  $\begin{array}{l}x+y=12\\ 3x+y=30\end{array}$

The given options:

F. $3$ G. $-1$ H. $1$ J. $-6$

Calculation :

As per problem,

Consider the given system of equations:

  $\begin{array}{l}x+y=12\\ 3x+y=30\end{array}$

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

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}\text{}x+y=12\text{ [Write the first equation]}\\ x+y-y=12-y\text{ [Subtract }y\text{ from each side]}\\ x=12-y\text{ [Simplify}]\end{array}$

Find the value of $y$ by substituting $12-y$ for $x$ in the second equation.

  $\begin{array}{l}\text{ 3}x+y=30\text{ [Write the second equation]}\\ \text{3(12}-y)+y=30\text{ [Substitute }x=12-y\text{]}\\ 36-3y+y=30\text{ [Distributive property}]\\ 36-2y=30\text{ [Combine like terms}]\\ 36-2y-36=30-36\text{ [Subtract 36 from each side}]\\ -\text{2}y=-6\text{ [Simplify}]\\ y=3\text{ [Divide both sides by }-\text{2}]\end{array}$

So, $y=3$ .

Thus, $-2y=-2(3)=-6$ .