Chapter 6.3, Problem 16PPE

To determine

To solve: The system of linear equations using elimination.

Answer to Problem 16PPE

x = 1 and y = 2

Explanation of Solution

Given information:

The equations $3x+y=5$ and $2x-2y=-2$

Calculation:

Multiply equation $3x+y=5$ by 2 to obtain

  $\begin{array}{l}3x+y=5\\ \Rightarrow 2\left(3x+y\right)=2\times 5\\ \Rightarrow 6x+2y=10\end{array}$

Now add equation $2x-2y=-2$ and $6x+2y=10$ to obtain

  $\begin{array}{l}2x-2y=-2\\ \underset{\_}{6x+2y=10}\\ 8x+0=8\end{array}$

Now simplify above equation.

  $\begin{array}{l}8x+0=8\\ \Rightarrow x=1\end{array}$

Use above value ofx in equation $2x-2y=-2$

  $\begin{array}{c}2\left(1\right)-2y=-2\\ -2y=-2-2\\ -2y=-4\\ y=2\end{array}$

Therefore the solution is x = 1 and y = 2.