Question

directions: if l || m, solve for x and y.

Explanation:

Step1: Identify angle - relationship

Since \(l\parallel m\), the corresponding angles are equal. So, \(9x + 25=13y - 19\) and the alternate - interior angles are equal, so \(9x + 25=17y+5\).

Step2: Set up a system of equations

We have the system of equations:
\(

$$\begin{cases}9x+25 = 13y - 19\\9x+25 = 17y+5\end{cases}$$

\)
From the first equation \(9x=13y - 44\), from the second equation \(9x=17y - 20\).
Then \(13y - 44=17y - 20\).

Step3: Solve for \(y\)

Subtract \(13y\) from both sides: \(-44 = 4y-20\).
Add 20 to both sides: \(4y=-24\), so \(y = - 6\).

Step4: Solve for \(x\)

Substitute \(y = - 6\) into \(9x=13y - 44\).
\(9x=13\times(-6)-44\).
\(9x=-78 - 44=-122\).
\(x=-\frac{122}{9}\)

Answer:

\(x =-\frac{122}{9},y=-6\)