Chapter 11, Problem 5MS

To determine

To find: The solution of the given equations.

Answer to Problem 5MS

The solution of the given equations is $x=\frac{1}{2},y=\frac{1}{3}$ .

Explanation of Solution

Given information:

The equation is $2x+3y=2,8x+9y=7$ .

Calculation:

Consider the equations.

  $2x+3y=2$ ..... (1)

Consider the equations.

  $8x+9y=7$ ..... (2)

Multiply by 4 in equation (1) .and subtract equation (2)

  $\begin{array}{l}\underset{\_}{\begin{array}{c}8x+12y=8\\ 8x+9y=7\end{array}}\\ 3y=1\\ y=\frac{1}{3}\end{array}$

Substitute $y=\frac{1}{3}$ in above equation.

  $\begin{array}{c}2x+3\left(\frac{1}{3}\right)=2\\ 2x=2-1\\ x=\frac{1}{2}\end{array}$

Thus, the solution of equation is $x=\frac{1}{2},y=\frac{1}{3}$ .