Chapter 2.4, Problem 42E

To determine

To select: the correct value for $2x+2y$ from the given options.

Answer to Problem 42E

B. 4

Explanation of Solution

Given information:

The given equation is as follows:

  $2x+y=12$… (1)

  $x+2y=-6$… (2)

The options are as follows:

  $\begin{array}{l}\text{A 0}\\ \text{B }4\\ \text{C 8}\\ \text{D 12}\\ \text{E 14}\end{array}$

Calculation:

Solve equation (1) for y as shown below.

  $\begin{array}{c}2x+y=12\\ y=12-2x\end{array}$… (3)

Put the value of y in equation (2) and evaluate x as follows:

  $\begin{array}{c}x+2\left(12-2x\right)=-6\\ x+24-4x=-6\\ -3x+24=-6\\ -3x=-6-24\\ -3x=-30\\ x=\frac{-30}{-3}\\ =10\end{array}$

Put the value of x in equation (2) and evaluate y as follows:

  $\begin{array}{c}y=12-2x\\ =12-2\left(10\right)\\ =12-20\\ =-8\end{array}$

Put the values of x and y in $2x+2y$ and solve as follows:

  $\begin{array}{c}2x+2y=2\left(10\right)+2\left(-8\right)\\ =20-16\\ =4\end{array}$

The value of $2x+2y$ is 4. Thus, option B is correct.