Question

1. \

$$\begin{cases} 2x + y = -2 \\\\ 5x + 3y = -8 \\end{cases}$$

Explanation:

Step1: Solve for y from first equation

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

Step2: Substitute y into second equation

Substitute \(y = -2 - 2x\) into \(5x + 3y = -8\):
\(5x + 3(-2 - 2x) = -8\)
Simplify: \(5x - 6 - 6x = -8\)
Combine like terms: \(-x - 6 = -8\)
Add 6 to both sides: \(-x = -2\)
Multiply by -1: \(x = 2\).

Step3: Find y using x=2

Substitute \(x = 2\) into \(y = -2 - 2x\):
\(y = -2 - 2(2) = -2 - 4 = -6\).

Answer:

The solution to the system is \(x = 2\), \(y = -6\) (or as an ordered pair \((2, -6)\)).