Chapter 6.3, Problem 18PPE

To determine

To solve: The system of linear equations using elimination.

Answer to Problem 18PPE

x = 3 and y = 4

Explanation of Solution

Given information:

The equations $3x+2y=17$ and $2x+5y=26$

Calculation:

Multiply equation $3x+2y=17$ by 2 to obtain

  $\begin{array}{l}3x+2y=17\\ \Rightarrow 2\left(3x+2y\right)=2\times 17\\ \Rightarrow 6x+4y=34\mathrm{...}\left(1\right)\end{array}$

Multiply equation $2x+5y=26$ by 3 to obtain

  $\begin{array}{l}2x+5y=26\\ \Rightarrow 3\left(2x+5y\right)=3\times 26\\ \Rightarrow 6x+15y=78\mathrm{...}\left(2\right)\end{array}$

Now subtract equation (1)from (2)to obtain

  $\begin{array}{l}6x+15y=78\\ \underset{\_}{6x+4y=34}\\ 0+11y=44\end{array}$

Now simplify above equation.

  $\begin{array}{l}0+11y=44\\ \Rightarrow y=4\end{array}$

Use above value ofy in equation $2x+5y=26$

  $\begin{array}{c}2x+5\left(4\right)=26\\ 2x=26-20\\ 2x=6\\ x=3\end{array}$

Therefore the solution is x = 3 and y = 4.