Chapter 9.4, Problem 10WE

To determine

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

Answer to Problem 10WE

The solution is $\left(-10,3\right)$ .

Explanation of Solution

Given:

The equations are $-3x+5y=45$ and $3x+13y=9$ .

Calculation:

Let $-3x+5y=45$ be equation (1) and $3x+13y=9$ be equation (2).

Observe that equation (1) has a term $-3x$ and equation (2) has a term $3x$ . So, addition of the two equations will be easier to obtain the solution of the set.

  $\begin{array}{l}\cancel{-3x}+5y=45\\ \underset{\_}{\cancel{3x}+13y=9}\\ \text{ 18}y=54\\ y=3\left[\text{Dividing both sides by 18}\right]\end{array}$

Substitute 3 for y in equation (1) and solve for x .

  $\begin{array}{c}-3x+5\left(3\right)=45\\ -3x+15=45\\ -3x=30\left[\text{Subtracting 15 on both sides}\right]\\ x=-10\left[\text{Dividing both sides by 3}\right]\end{array}$

So, the solution of the given equations is $\left(-10,3\right)$ .