Chapter 7.2, Problem 16E

To determine

To solve: The system of linear equations $x+5y=10\text{and}3x-10y=-5$ by elimination method and check the solution.

Answer to Problem 16E

The solution of system of linear equations is $\left(3,\frac{7}{5}\right)$ .

Explanation of Solution

Given:

System of linear equations is:

  $\begin{array}{l}x+5y=10\mathrm{......}\left(1\right)\\ 3x-10y=-5\mathrm{......}\left(2\right)\end{array}$

Calculation:

Multiply equation (1) by 3 as follows:

  $\begin{array}{l}3\left(x+5y=10\right)\\ 3x+15y=30\mathrm{......}\left(3\right)\end{array}$

Solve the equation (3) and (2) by elimination method as follows:

  $\begin{array}{l}\underset{\_}{\begin{array}{l}3x+15y=30\\ -\left(3x-10y=-5\right)\end{array}}\\ 0+25y=35\\ y=\frac{7}{5}\end{array}$

Substitute $\frac{7}{5}$ for y in equation (2) as follows:

  $\begin{array}{c}3x-10\left(\frac{7}{5}\right)=-5\\ x=\frac{9}{3}\\ =3\end{array}$

Thus, the solution of system of linear equations is $\left(3,\frac{7}{5}\right)$ .

Check the solution by substituting $\left(3,\frac{7}{5}\right)$ in equation (1) as follows:

  $\begin{array}{c}3+5\left(\frac{7}{5}\right)=10\\ 10=10\end{array}$

Thus, the solution is satisfying the system of equations.