Question

find the values of x and y.

Explanation:

Step1: Use the property of similar - triangles (assuming similar - side ratios).

Since the two triangles are similar (by the parallel - side property indicated by the arrows), the ratios of corresponding sides are equal. We can set up the following two equations based on the proportionality of the sides:
For the vertical sides: $x + 3=\frac{3}{2}x+2$.
For the horizontal sides: $2y - 1=3y - 5$.

Step2: Solve the equation for \(x\).

\[

$$\begin{align*} x + 3&=\frac{3}{2}x+2\\ x-\frac{3}{2}x&=2 - 3\\ \frac{2x-3x}{2}&=-1\\ -\frac{x}{2}&=-1\\ x&=2 \end{align*}$$

\]

Step3: Solve the equation for \(y\).

\[

$$\begin{align*} 2y - 1&=3y - 5\\ 2y-3y&=-5 + 1\\ -y&=-4\\ y&=4 \end{align*}$$

\]

Answer:

$x = 2$
$y = 4$