Chapter 5, Problem 1CT

To determine

To Solve: the system of linear equation.

Answer to Problem 1CT

  $x=-3,y=5.$

Explanation of Solution

Given information: We have given a system of linear equation:

  $\begin{array}{l}Equation\text{ 1: }8x+3y=-9\\ Equation\text{ 2:}-8x+y=29.\end{array}$

Calculation:

To solve this system of equation we use elimination method. According to an Elimination Method we eliminate a variable from the equation by adding or subtracting system of equations and solve.

Adding equations:

  $\frac{\begin{array}{l}8x+3y=-9\\ -8x+y=29\end{array}}{\text{ 4}y\text{ = 20}}$

Divide by 4 on both sides.

  $\frac{\text{4}y}{4}\text{ = }\frac{\text{20}}{4}$

  $y=5$

Now, plug the value y=5in equation 1

  $8x+3y=-9$

  $8x+3\left(5\right)=-9$

  $8x+15=-9$

Subtract 15 on both sides

  $8x+15-15=-9-15$

  $8x=-24$

Divide by 8 on both sides.

  $\frac{8x}{8}=-\frac{24}{8}$

  $x=-3$

Therefore, the values of $x\text{ and }y$ are -3 and 5.