Chapter 6.3, Problem 25PPS

To determine

To solve the system of equations using elimination method

Answer to Problem 25PPS

  $x=2$

  $y=-1$

Explanation of Solution

Given:

Equations:

  $\begin{array}{l}3x-5y=11\\ 5(x+y)=5\end{array}$

Calculation:

Let the equations be numbered as

  $3x-5y=11\to \text{(1)}$

  $5(x+y)=5\to \text{(2)}$

Expand equation (2) as follows:

  $5x+5y=5\to \text{(3)}$

Add (1) and (2), so that y is eliminated.

  $\begin{array}{l}3x-5y=11\\ \frac{5x+5y=5}{8x=16}\end{array}$

  $\begin{array}{l}8x=16\\ x=\frac{16}{8}\text{ [Divide 8 on both sides]}\\ x=2\end{array}$

Substitute $x=2$ in any one of the equations.

Say, equation (1)

  $\begin{array}{c}3(2)-5y=11\\ 6-5y=11\text{ [Subtracting 6 on both sides]}\\ -5y=11-6\\ -5y=5\\ y=\frac{5}{-5}\text{ [Dividing }-5\text{ both sides]}\\ y=-1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=2$ and $y=-1.$