Chapter 6.4, Problem 9P

Solve each system. Explain why you chose the method you used.

$2y=x+1$

$-2x-y=7$

To determine

To solve the given equation.

Answer to Problem 9P

The solution is (-3, -1)

Explanation of Solution

Given information :

Given equations are,

  $\begin{array}{l}2y=x+1\\ -2x-y=7\end{array}$

Here we shall use the elimination method by making y coefficient same and then eliminating by adding both equations. We shall use elimination because it is easy to eliminate one variable just by adding the equations here.

Multiply second equation with 2 and then add both equations we get,

  $\begin{array}{c}2y+2\left(-2x-y\right)=x+1+14\\ 2y-4x-2y=x+15\\ -4x=x+15\\ -5x=15\\ x=-3\end{array}$

Now put $x=-3$ in any equation we get,

  $\begin{array}{l}2y=\left(-3\right)+1\\ 2y=-2\\ y=-1\end{array}$

Hence the solution is (-3, -1)