Question 1

Which of the following graphs best represents the solution set to the system of inequalities $$y \leq \frac{2}{3}x + 6$$ and $$y \u003c 3x + 3$$?

Accepted Answer

The fourth image (bottom right): The region between two slanted lines, colored magenta on the left, black in the middle, and cyan on the right.

Question 2

Which image best represents the solution set to the system $$y \geq x + 2x + 1$$ and $$y \u003c \frac{x}{2} - 2$$?

Accepted Answer

The fifth image (bottom row, first): The cyan region above a parabola and below a line.

Question 3

Which image shows the solution set for the system $$7x - 4y \geq 28$$ and $$-7x + 4y \geq 28$$?

Accepted Answer

The third image (bottom left): The gray region between two parallel lines.

Question 4

Which image best represents the solution set to the system $$y \u003c 3x + 3$$?

Accepted Answer

The first image (top left): The yellow region below a slanted line.

Question 5

Which image best represents the solution set to the system $$y \leq \frac{2}{3}x + 6$$?

Accepted Answer

The first image (top left): The yellow region below a slanted line.

Question 6

Which image best represents the solution set to the system $$y \geq x^2$ + 2x + 1$$ and $$y \u003c \frac{x}{2} - 2$$?

Accepted Answer

The fifth image (bottom row, first): The cyan region above a parabola and below a line.

Question 7

Which image best represents the solution set to the system $$y  -x^2$?

Accepted Answer

The sixth image (bottom row, second): The cyan region between two parabolas.

Question 8

Which image best represents the solution set to the system $$y \u003e x^2$ and y$$ \u003c $$-x^2$$?

Accepted Answer

None of the images represent this solution set, as there is no region where $$y \u003e x^2$ and y$$ \u003c $$-x^2$$ simultaneously.

College Algebra: Systems of Equations, Inequalities, and Matrices – Step-by-Step Study Guidance

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