Chapter 0.8, Problem 14E

To determine

To solve the given system of equation.

Answer to Problem 14E

  $x=1.24$ and $y=0.35$

Explanation of Solution

Given information:

The system of equations are,

  $\begin{array}{l}4x-7y=8\\ -2x+5y=-1\end{array}$

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,

  $4x=8+7y$

Cross-multiplying,

  $x=\frac{8}{4}-\frac{7y}{4}$

On solving,

  $x=2-\frac{7y}{4}$ _____________(1)

Substituting (1) in the 2^nd equation,

  $-2(2-\frac{7y}{4})+5y=-1$

Opening the brackets,

  $-4+\frac{7y}{2}+5y=-1$

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

  $\frac{7y}{2}+5y=-1+4$

On solving,

  $\frac{17y}{2}=3$

Cross-multiplying,

  $y=\frac{2\times 3}{17}$

On solving,

  $y=0.35$

Substituting in (1),

  $x=2-\frac{7(0.35)}{2}$

On solving,

  $x=1.24$

Hence, the solution to the system of equation is,

  $x=1.24$ and $y=0.35$