Chapter 5.2, Problem 16E

To determine

To solve: The system of linear equations

Answer to Problem 16E

The possible solution of the system is the ordered pair $\left(x,y\right)=\left(0,2\right)$

Explanation of Solution

Given:

  $\begin{array}{l}11x-7y=-14\\ x-2y=-4\end{array}$

Calculation:

  $\begin{array}{l}11x-7y=-14\\ x-2y=-4\end{array}$

Solve the equation $x-2y=-4$ for $x$

  $\begin{array}{l}11x-7y=-14\\ x=-4+2y\end{array}$

Substitute the value of $x$ in the equation $11x-7y=-14$

  $11(-4+2y)-7y=-14$

Distribute $11$ through the parenthesis

  $-44+22y-7y=-14$

Collect like terms

  $-44+15y=-14$

Move constant $-44$ to the right side and change its sign

  $15y=-14+44$

  $15y=30$

Distribute both sides by $15$

  $y=2$

Substitute the value of $y$ in the equation $x=-4+2y$

  $x=-4+2\times 2$

Solve the equation for $x$

  $x=0$

The possible solution of the system is the ordered pair $\left(x,y\right)=\left(0,2\right)$

Check if the ordered pair is the solution of the system of equations

  $\begin{array}{l}11\times 0-7\times 2=-14\\ 0-2\times 2=-4\end{array}$

Simplify the equalities

  $\begin{array}{l}-14=-14\\ -4=-4\end{array}$

Conclusion:

Hence, the possible solution of the system is the ordered pair $\left(x,y\right)=\left(0,2\right)$