91Ó°ÊÓ

Consider the figure.

Here from the figure, there are four parallel lines.

Thus,if three parallel lines cut of a congruent segment on a transversal then they cut of the congruent segment on every transversal.

Therefore, the theorem states thatif three parallel lines cut of the congruent segment on a transversal then they cut of a congruent segment on every transversal.

Consider the figure.

Use theorem which states that if three parallel lines cut of the congruent segment on a transversal then they cut of the congruent segment on every transversal.

Corresponding alternate exterior angles are congruent.

Thus, simplify the equations as follows:

$\begin{array}{c}3x−7=11\\ 3x=11+7\\ 3x=18\\ x=6\end{array}$

Similarly, simplify the equation as follows:

$\begin{array}{c}5x−y=11\\ 5\left(6\right)−y=11\\ 30−y=11\\ −y=11−30\\ y=19\end{array}$

Thus, the values are $x=6,y=19$.