Chapter 0.8, Problem 12E

To determine

To solve the given system of equation.

Answer to Problem 12E

  $x=1.6$ and $y=0.6$

Explanation of Solution

Given information:

The system of equations are,

  $\begin{array}{l}3x-2y=6\\ 5x-5y=5\end{array}$

Formula used:

Substitution

Calculation:

Method used to solve the system of equation is substitution.

In equation 1, writing x in terms of y.

Shifting left hand side terms to right-hand side,

  $3x=6+2y$

Cross-multiplying,

  $x=\frac{6}{3}-\frac{2y}{3}$

On solving,

  $x=2-\frac{2y}{3}$ _____________(1)

Substituting (1) in the 2^nd equation,

  $5(2-\frac{2y}{3})-5y=5$

Opening the brackets,

  $10-\frac{10y}{3}-5y=5$

Shifting left- hand side values to right- hand side,

  $-\frac{10y}{3}-5y=5-10$

On solving,

  $-\frac{25y}{3}=-5$

Cross-multiplying,

  $y=\frac{-5\times 3}{-25}$

On solving,

  $y=0.6$

Substituting in (1),

  $x=2-\frac{2(0.6)}{3}$

On solving,

  $x=1.6$

Hence, the solution to the system of equation is,

  $x=1.6$ and $y=0.6$