Question

Find the values of x and y that make these triangles congruent by the HL Theorem.

x=2, x=3
x=3, y=2
x=1, y=2
x=2, y=1

Answer 1

You should have a system of equations:

x + 5 = y - x [eq 1]

y + 5 = 3y + x [eq 2]

solve eq 1 for y

y = 2x + 5

Eq 2: 2y = 5 - x

substitute this expression for y in eq 2

2(2x + 5) = 5 - x

expand, combine like terms, solve for x

x = - 1

y = 3

Answer 2

but there is no y=3 wen x=1 /: