Chapter 11.1, Problem 37AYU

To determine

The solution of the system of linear equations $\{\begin{array}{ccccc}3x& -& 6y& =& 7\\ 5x& -& 2y& =& 5\end{array}$ .

Answer to Problem 37AYU

Solution:

The solution of the system is $x=\frac{2}{3}$ and $y=-\frac{5}{6}$

Explanation of Solution

Given information:

The system of linear equations $\{\begin{array}{ccccc}3x& -& 6y& =& 7\\ 5x& -& 2y& =& 5\end{array}$

The given system of linear equation is

  $\{\begin{array}{ccccc}3x& -& 6y& =& 7\\ 5x& -& 2y& =& 5\end{array}$ .

To solve this system using elimination method, first multiply the equation $3x-6y=7$ by $5$ and equation $5x-2y=5$ by $3$ .

  $15x-30y=35$ ----- (1)

  $15x-6y=15$ ------(2)

Subtractthe equation (2) from(1) to eliminate the variable.

  $\begin{array}{cccccc}& 15x& -& 30y& =& 35\\ -& 15x& -& 6y& =& 15\\ & & & -24y& =& 20\end{array}$

Solve for $y$ , for that, divide both sides by $-24.$

  $\frac{-24y}{-24}=\frac{20}{-24}$

  $\Rightarrow y=-\frac{20}{24}$

  $\Rightarrow y=-\frac{5}{6}$ .

Substitute $y=-\frac{5}{6}$ in equation $3x-6y=7.$

  $3x-6\left(-\frac{5}{6}\right)=7.$

  $\Rightarrow 3x+5=7$ .

Subtract $5$ from both sides.

  $\Rightarrow 3x+5-5=7-5$

  $\Rightarrow 3x=2$

  $\Rightarrow x=\frac{2}{3}$ .

Therefore, the solution of system of equation $\{\begin{array}{ccccc}3x& -& 6y& =& 7\\ 5x& -& 2y& =& 5\end{array}$ is $x=\frac{2}{3},y=-\frac{5}{6}$ .