Chapter 3, Problem 17SGR

To determine

To calculate: The solution set for the system of equations with the help either substitution or elimination.

  $\begin{array}{c}5x-2y=4\\ -2y+x=12\end{array}$

Answer to Problem 17SGR

The solution set for the system of equations is $\left(-2,-7\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{c}5x-2y=4\\ -2y+x=12\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{c}5x-2y=4\\ -2y+x=12\end{array}$

Use the method of substitution to solve the system above.

From the equation $5x-2y=4$ isolate the value of y ,

  $\begin{array}{c}5x-2y=4\\ -2y=4-5x\\ y=\frac{4-5x}{-2}\end{array}$

Now substitute $y=\frac{4-5x}{-2}$ in the equation $-2y+x=12$ ,

  $\begin{array}{c}-2\left(\frac{4-5x}{-2}\right)+x=12\\ 4-5x+x=12\\ 4-4x=12\\ -4x=8\end{array}$

Simplify it further as,

  $\begin{array}{c}-4x=8\\ x=-2\end{array}$

Now, substitute $x=-2$ in the equation $y=\frac{4-5x}{-2}$ ,

  $\begin{array}{c}y=\frac{4-5\left(-2\right)}{-2}\\ y=\frac{4+10}{-2}\\ y=\frac{14}{-2}\\ y=-7\end{array}$

Therefore, solution is the coordinate pair, $\left(-2,-7\right)$ .

Thus, the solution set for the system of equations is $\left(-2,-7\right)$ .