Question

i
j
h
q
r
p
12y + x - 48
13x - 18
8x + y + 10
11x
x=
=
submit
work it out

Explanation:

Step1: Set up the equation for equal - length sides

Assume the two right - angled triangles are congruent. Then \(13x - 18=11x\).
Subtract \(11x\) from both sides: \(13x-11x - 18=11x-11x\), which gives \(2x-18 = 0\).
Add \(18\) to both sides: \(2x=18\).
Divide both sides by \(2\): \(x = 9\).

Step2: Substitute \(x\) into the other equation

Substitute \(x = 9\) into \(12y+x - 48=8x+y + 10\).
We get \(12y+9-48=8\times9+y + 10\).
Simplify: \(12y - 39=72+y + 10\).
Subtract \(y\) from both sides: \(12y-y-39=72 + 10\).
\(11y-39=82\).
Add \(39\) to both sides: \(11y=82 + 39\), so \(11y=121\).
Divide both sides by \(11\): \(y = 11\).

Answer:

\(x = 9\), \(y = 11\)