Chapter 0.8, Problem 13E

To determine

To solve the given system of equation.

Answer to Problem 13E

  $x=3$ and $y=0$

Explanation of Solution

Given information:

The system of equations are,

  $\begin{array}{l}3y+x=3\\ -2y+5x=15\end{array}$

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,

  $x=3-3y$ _____________(1)

Substituting (1) in the 2^nd equation,

  $-2y+5(3-3y)=15$

Opening the brackets,

  $-2y+15-15y=15$

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

  $-17y=15-15$

On solving,

  $-17y=0$

On solving,

  $y=0$

Substituting in (1),

  $x=3-3(0)$

On solving,

  $x=3$

Hence, the solution to the system of equation is,

  $x=3$ and $y=0$