Question

1. \

$$\begin{cases} 3x - 2y = 7 \\\\ x + 3y = -5 \\end{cases}$$

Explanation:

Step1: Solve the second equation for \( x \)

From \( x + 3y = -5 \), we get \( x = -5 - 3y \).

Step2: Substitute \( x = -5 - 3y \) into the first equation

Substitute into \( 3x - 2y = 7 \):
\( 3(-5 - 3y) - 2y = 7 \)

Step3: Simplify and solve for \( y \)

Expand: \( -15 - 9y - 2y = 7 \)
Combine like terms: \( -15 - 11y = 7 \)
Add 15 to both sides: \( -11y = 22 \)
Divide by -11: \( y = -2 \)

Step4: Substitute \( y = -2 \) back into \( x = -5 - 3y \)

\( x = -5 - 3(-2) = -5 + 6 = 1 \)

Answer:

The solution to the system is \( x = 1 \), \( y = -2 \)