Question

1. \

$$\begin{cases} x - 5y = 2 \\\\ 9x + 8 = 15y \\end{cases}$$

Explanation:

Step1: Express x from first equation

From \( x - 5y = 2 \), we get \( x = 5y + 2 \).

Step2: Substitute x into second equation

Substitute \( x = 5y + 2 \) into \( 9x + 8 = 15y \):
\( 9(5y + 2) + 8 = 15y \)
Expand: \( 45y + 18 + 8 = 15y \)
Simplify: \( 45y + 26 = 15y \)
Subtract \( 15y \) and 26: \( 30y = -26 \)
Divide: \( y = -\frac{13}{15} \)

Step3: Find x using y

Substitute \( y = -\frac{13}{15} \) into \( x = 5y + 2 \):
\( x = 5(-\frac{13}{15}) + 2 \)
Simplify: \( x = -\frac{13}{3} + 2 = -\frac{13}{3} + \frac{6}{3} = -\frac{7}{3} \)

Answer:

\( x = -\frac{7}{3} \), \( y = -\frac{13}{15} \)