Chapter 8.4, Problem 81SPR

To determine

The value of x and y.

Answer to Problem 81SPR

  $x=1$

  $y=\frac{3}{2}$

Explanation of Solution

Given:

The given figure will be:

Calculation:

Using Corollary of Congruent Parts of Parallel lines

  $\begin{array}{l}2x+3=6-x\mathrm{..........}\left(1\right)\\ \frac{4}{3}y+1=2y\mathrm{.................}\left(2\right)\end{array}$

The equation 1 can be solved as:

  $\begin{array}{l}2x+3=6-x\\ 2x+x=6-3\\ 3x=3\\ x=1\end{array}$

The equation 2 can be solved as:

  $\begin{array}{l}\frac{4}{3}y+1=2y\\ \frac{4}{3}y-2y=-1\\ y=\frac{3}{2}\end{array}$