Chapter 9.5, Problem 20WE

To determine

To find: The solution of the given equations by addition or subtraction method.

Answer to Problem 20WE

The solution of the given equations by addition or subtraction methodis $a=\frac{7}{6},b=-\frac{13}{10}$

Explanation of Solution

Given information:

The equationis $18a-5b=17,6a+10b=-6$ .

Calculation:

Consider the equations.

  $18a-5b=17$ ……. (1)

Consider the equations.

  $6a+10b=-6$ ……. (2)

Multiply equation(2) by 5 and equation (1) by10 and add.

  $\begin{array}{l}\underset{\_}{\begin{array}{c}180a-50b=170\\ 30a+50b=-30\end{array}}\\ 120a=140\\ a=\frac{7}{6}\end{array}$

Substitute $a=\frac{7}{6}$ in above equation.

  $\begin{array}{l}6\left(\frac{7}{6}\right)+10b=-6\\ 7+10b=-6\\ 10b=-13\\ b=-\frac{13}{10}\end{array}$

Thus, the solution of equation is $a=\frac{7}{6},b=-\frac{13}{10}$ .