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 \(x\).

$$
LATEXBLOCK0
$$

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

$$
LATEXBLOCK1
$$

Answer:

$x = 2$
$y = 4$