Question

1. (a.ei.2, 10 points)

the solutions to a system of linear inequalities and points f, g, h, j, k, l, m, and n are shown. all labeled points have integral coordinates.

• points f, j, and m each lie on a boundary line.
• point g lies on both boundaries.

circle each labeled point that represents a solution to this system of linear inequalities.

1. (a.ei.2, 10 points)

circle 4 ordered pairs that are solutions to this system of inequalities.
\

$$\begin{cases} y > -2x - 1 \\\\ y \\leq 5x - 4 \\end{cases}$$

answer choices
(-4, 3) (0, 4) (1, 1) (1, -3)
(3, -1) (4, 3) (6, 0) (-4, -4)

1. (a.ei.2, 5 points)

what is the solution for this system of equations? fill in the solution as an ordered pair.
\

$$\begin{cases} y = -2x - 1 \\\\ 3x - y = 11 \\end{cases}$$

solution is (\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_, \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_)

1. (a.ei.2, 5 points)

given the following system of equations, what is the solution for x?
\

$$\begin{cases} 4x - 3y = 11 \\\\ 3x + 2y = -1 \\end{cases}$$

x = \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_

Explanation:

Step1: Substitute \( y = -2x - 1 \) into \( 3x - y = 11 \)

Substitute \( y \) in the second equation: \( 3x - (-2x - 1) = 11 \)
Simplify: \( 3x + 2x + 1 = 11 \)
Combine like terms: \( 5x + 1 = 11 \)

Step2: Solve for \( x \)

Subtract 1 from both sides: \( 5x = 11 - 1 = 10 \)
Divide by 5: \( x = \frac{10}{5} = 2 \)

Step3: Solve for \( y \)

Substitute \( x = 2 \) into \( y = -2x - 1 \): \( y = -2(2) - 1 = -4 - 1 = -5 \)

Answer:

(2, -5)