Chapter 9.4, Problem 20WE

To determine

To solve: The given equations by the addition-or-subtraction method.

Answer to Problem 20WE

The solution is $\left(2,0\right)$ .

Explanation of Solution

Given:

The equations are $x-5y=2$ and $2x+y=4$ .

Calculation:

Let $x-5y=2$ be equation (1) and $2x+y=4$ be equation (2).

Multiply equation (2) by 5.

  $\begin{array}{c}5\left(2x+y\right)=5\left(4\right)\\ 10x+5y=20\end{array}$

Let $10x+5y=20$ be equation (3).

Observe that equation (1) has a term $-5y$ and equation (3) has a term $5y$ . So, adding the two equations will be easier to obtain the solution of the set.

  $\begin{array}{l}x-\cancel{5y}=2\\ \underset{\_}{10x+\cancel{5y}=20}\\ 11x=22\\ x=2\left[\text{Dividing both sides by 11}\right]\end{array}$

Substitute 2 for x in equation (1) and solve for y .

  $\begin{array}{c}\left(2\right)-5y=2\\ 2-5y=2\\ -5y=0\left[\text{Subtracting 2 on both sides}\right]\\ y=0\left[\text{Dividing both sides by }-5\right]\end{array}$

So, the solution of the given equations is $\left(2,0\right)$ .