Question

Find the value of the variables make the hypotonuses congruent and the legs congruent

Answer 1

x = -1

y = 3

Step-by-step explanation:

If the hypothenuse and the legs are congruent, we can write the following equations:

3y + x = y + 5

y - x = x + 5

So, taking the second equation and solving for y, we get:

`\begin{gathered} y-x+x=x+5+x \\ y=2x+5 \end{gathered}`

Replacing y on the first equation:

`\begin{gathered} 3y+x=y+5 \\ 3(2x+5)+x=(2x+5)+5 \end{gathered}`

So, solving for x, we get:

`\begin{gathered} 3(2x)+3(5)+x=2x+5+5 \\ 6x+15+x=2x+10 \\ 7x+15=2x+10 \\ 7x+15-2x=2x+10-2x \\ 5x+15=10 \\ 5x+15-15=10-15 \\ 5x=-5 \\ (5x)/(5)=-(5)/(5) \\ x=-1 \end{gathered}`

So, the value of y is:

`\begin{gathered} y=2x+5 \\ y=2(-1)+5 \\ y=-2+5 \\ y=3 \end{gathered}`

Therefore, the values of x is -1 and the value of y is 3