Chapter 8.5, Problem 30STP

To determine

To select:

The correct option to show the solution of set of equations $\begin{array}{l}2x-4y=-12\\ -x+4y=8\end{array}$ :

F. $\left(4,4\right)$

H. $\left(-4,-4\right)$

G. $\left(-4,1\right)$

J. $\left(1,-4\right)$

Answer to Problem 30STP

The correct option is G. The solution of set of equations $\begin{array}{l}2x-4y=-12\\ -x+4y=8\end{array}$ is $\left(-4,1\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}2x-4y=-12\\ -x+4y=8\end{array}$

Calculation:

The set of equations is given as:

  $2x-4y=-12$  … (1)

  $-x+4y=8$  … (2)

Add these two equations to calculate the value of $x$ :

  $\begin{array}{l}2x-4y-x+4y=-12+8\\ x=-4\end{array}$

Now, put value of $x$ in eq. (1):

  $\begin{array}{l}2x-4y=-12\\ 2\left(-4\right)-4y=-12\\ -8-4y=-12\\ -4y=-4\\ y=1\end{array}$

So, the solution set of the given set of equations is $\left(x,y\right)=\left(-4,1\right)$ . The correct option is G.