Chapter 6.3, Problem 10PPE

To determine

To solve:The pair of equations

  $\begin{array}{l}4x-7y=3\\ x-7y=-15\end{array}$

Answer to Problem 10PPE

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

Explanation of Solution

Given information:

  $\begin{array}{l}4x-7y=3\mathrm{...}\left(i\right)\\ x-7y=-15\mathrm{...}\left(ii\right)\end{array}$

Calculation:

Solve the equation using elimination method:

  $\begin{array}{l}4x-7y=3\\ \underset{\_}{\begin{array}{l}x-7y=-15\\ -++\end{array}}\\ 4x-x-7y+7y=3+15\\ 3x=18\\ x=\frac{18}{3}\\ \boxed{x=6}\end{array}$

Put the value of $x$ in equation ( i )

  $\begin{array}{l}4\left(6\right)-7y=3\\ 24-7y=3\\ -7y=3-24\\ -7y=-21\\ y=\frac{-21}{-7}\\ \boxed{y=3}\end{array}$