Chapter 6.3, Problem 9P

Solve each system using elimination.

$2x-4y=-6$

$x-y=-1$

To determine

Solve the system of equation by elimination.

Answer to Problem 9P

$x=1,y=2$

Explanation of Solution

Given information:

We have given two equations:

  $\left[\begin{array}{c}2x-4y=-6\\ x-y=-1\end{array}\right]$

Calculation:

Solve the equations by using elimination method:

  $\left[\begin{array}{c}2x-4y=-6\\ x-y=-1\end{array}\right]$

Multiply $x-y=-1\text{by}2:2x-2y=-2$

$\left[\begin{array}{c}2x-4y=-6\\ 2x-2y=-2\end{array}\right]$

$\begin{array}{l}2x-2y=-2\\ -\\ \underset{\_}{2x-4y=-6}\\ 2y=4\end{array}$

$\left[\begin{array}{c}2x-4y=-6\\ 2y=4\end{array}\right]$

Solve $2y=4\text{for}y:$

$2y=4$

Divide both sides by 2:

$\frac{2y}{2}=\frac{4}{2}$

Simplify:

$y=2$

Now plug $y=2$ in $2x-4y=-6$ :

  $2x-4\cdot 2=-6$

  $2x-8=-6$

Add 8 from both sides:

$2x-8+8=-6+8$

$2x=2$

Divide both sides by 2:

$\frac{2x}{2}=\frac{2}{2}$

  $\text{Simplify}$

$x=1$

Therefore, the solutions of system is $x=1,y=2$