A company makes at most 100 units of product A and B combined per day. Product A requires 2 hours to make, and product B requires 1 hour. The company has at most 120 hours available per day. Which system of inequalities models this situation if $$x$$ is units of A and $$y$$ is units of B?

$$x + y \leq 100$$ , $$2x + y \leq 120$$

$$x + y \geq 100$$ , $$2x + y \leq 120$$

$$x + y \leq 100$$ , $$2x + y \geq 120$$

$$x + y \leq 120$$ , $$2x + y \leq 100$$

A concert hall can seat no more than 500 people. Tickets for adults ( $$x$$ ) cost \ $$20 and for children ($$ y $$) cost \$$ 10. The total revenue must be at least \$6,000. Which system of inequalities represents this situation?

$$x + y \leq 500$$ , $$20x + 10y \geq 6000$$

$$x + y \geq 500$$ , $$20x + 10y \leq 6000$$

$$x + y \leq 500$$ , $$20x + 10y \leq 6000$$

$$x + y \geq 500$$ , $$20x + 10y \geq 6000$$

A factory produces at least 200 gadgets and at most 400 widgets daily. Let $$x$$ be the number of gadgets and $$y$$ the number of widgets. Which of the following represents the constraints?

$$x \geq 200$$ , $$y \leq 400$$

$$x \leq 200$$ , $$y \geq 400$$

$$x \leq 400$$ , $$y \geq 200$$

$$x \geq 400$$ , $$y \leq 200$$

A school club is selling t-shirts ( $$x$$ ) and hats ( $$y$$ ). They must sell at least 30 items in total and at least twice as many t-shirts as hats. Which system of inequalities models this?

$$x + y \geq 30$$ , $$x \geq 2y$$

$$x + y \leq 30$$ , $$x \leq 2y$$

$$x + y \geq 30$$ , $$x \leq 2y$$

$$x + y \leq 30$$ , $$x \geq 2y$$

Which system of equations below has a solution where one of the variables is always the same value, no matter what the other variable is?

$$2x + 3y = 12$$ and $$x - y = 1$$

Which description best matches the solution region for the following system of inequalities? $$y \leq 3x - 2$$ $$y > -x + 1$$

The region below the line $$y = 3x - 2$$ and above the line $$y = -x + 1$$

The region above $$y = 3x - 2$$ and below $$y = -x + 1$$

col alg ar 9 test

Authored by LIZ SMITH

Mathematics

12th Grade

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Which of the following is a system of two linear inequalities?

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