Respuesta :

dionissenjo16

Answer:

x = 5, y = 6

Step-by-step explanation:

HL says that if the hypotenuse of two right triangles and one leg are congruent to each other, then the triangles are congruent. Therefore, we can write this as a system of equations:

x = y - 1 are the two congruent legs.

3x - 2 = 2y + 1 are the two congruent hypotenuses.

x = y - 1

Plug in y - 1 for x, and get:

3x - 2 = 2y + 1

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

3y - 3 - 2 = 2y + 1

3y - 5 = 2y + 1

y - 5 = 1

y = 6

Plugging in 6 for y, we get:

x = 6 - 1

x = 5

Therefore, x =  5, and y = 6.

KitdaAneek

Answer: 4th Option [tex]x=5, y=6[/tex]

Step-by-step explanation:

Based on the congruency statement, we know that these two triangles are equal and one corresponding side is equal to the other. That means that side CB = DE and side AC = DA. Since these side values have equations attached to them, let's use a system of equations to solve for x and y.

Solving:

Given : side CB = DE and side AC = DA, [tex]x=y-1[/tex] and [tex]3x-2=2y+1[/tex]

Line up the system:

[tex]x=y-1[/tex]

[tex]3x-2=2y+1[/tex]

Substitute [tex]y-1[/tex] for [tex]x[/tex] in  [tex]3x-2=2y+1[/tex]:

[tex]3(y-1)-2=2y+1[/tex]

Simplify:

[tex]3y-5=2y+1[/tex]

Subtract [tex]2y[/tex] from both sides :

[tex]3y-5-2y = 2y+1-2y[/tex]

Simplify:

[tex]y-5=1[/tex]

Add 5 to both sides:

[tex]y-5+5=1+5[/tex] → [tex]y=6[/tex]

Substitute 6 for [tex]y[/tex] in [tex]x=y-1[/tex]:

[tex]x=y-1[/tex]

[tex]x=(6)-1[/tex]

[tex]x=5[/tex]

Those are your two values, meaning the fourth option is correct.

That's it!