Question

1. \

$$\begin{cases} x + y = -4 \\\\ x - y = 2 \\end{cases}$$

Explanation:

Step1: Add the two equations

Add the equations \( x + y = -4 \) and \( x - y = 2 \) together. This will eliminate \( y \).

$$
LATEXBLOCK0
$$

Step2: Solve for \( x \)

Divide both sides of \( 2x = -2 \) by 2.

$$ x = \frac{-2}{2} = -1 $$

Step3: Substitute \( x \) into one equation

Substitute \( x = -1 \) into the first equation \( x + y = -4 \).

$$ -1 + y = -4 $$

Step4: Solve for \( y \)

Add 1 to both sides of the equation \( -1 + y = -4 \).

$$ y = -4 + 1 = -3 $$

Answer:

The solution to the system of equations is \( x = -1 \) and \( y = -3 \), or the ordered pair \( (-1, -3) \).