Chapter 4.4, Problem 63S

To determine

To solve: The system of the equations $4y+5x=21$ and $2x+7y=3$ .

Answer to Problem 63S

The solution is $\left(5,-1\right)$ .

Explanation of Solution

Given:

The equations are $4y+5x=21$ and $2x+7y=3$ .

Calculation:

The first equation is multiplied by $-2$ and the second equation by 5 then adds both the equations.

  $\begin{array}{l}-10x-8y=21\\ \underset{\_}{10x+35y=15}\\ 27y=-27\\ y=-1\end{array}$

Substitute $-1$ for $y$ in the equation $4y+5x=21$ .

  $\begin{array}{c}4\left(-1\right)+5x=21\\ -4+5x=21\\ 5x=25\\ x=5\end{array}$

Therefore, the solution is $\left(5,-1\right)$ .