Find the values of x and y that make these triangles congruent by the hl theorem

Option C x=2, y=6

Step-by-step explanation:

we know that

The hypotenuse leg theorem, (HL theorem), states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent

so

In this problem

Equate the hypotenuses of both right triangles

x+3=y-1 > x=y-4 > equation A

Equate the legs of both right triangles

y-3=2x-1 > equation B

substitute equation A in equation B and solve for y

y-3=2(y-4)-1

y-3=2y-8-1

2y-y=-3+9

y=6

Find the value of x

x=y-4 > x=6-4=2

therefore

x=2, y=6