Question

Question was provided via image upload.

Explanation:

Solve the system of equations algebraically

$$
LATEXBLOCK0
$$

$$ (3x + y) - (x + y) = 4 - (-2) \implies 2x = 6 \implies x = 3 $$

$$ 3 + y = -2 \implies y = -5 $$

Determine values for the tables of values

For \(3x + y = 4 \implies y = -3x + 4\):

$$
LATEXBLOCK1
$$

For \(x + y = -2 \implies y = -x - 2\):

$$
LATEXBLOCK2
$$

Identify the graphical solution

The intersection point of the two lines is \((3, -5)\).

Answer:

The solution to the system of linear equations is:

$$ (x, y) = (3, -5) $$

The tables of values for each equation are:
For \(3x + y = 4\):

$$
LATEXBLOCK0
$$

For \(x + y = -2\):

$$
LATEXBLOCK1
$$

The graph of the system consists of two lines intersecting at the point \((3, -5)\).