Graphing Linear Inequalities and Systems of Inequalities: Algebra 1 Math Test – PDF Download

Question 1: Test two points (2 points)

Consider the inequality \(y>2x-3\).

1. Determine whether \((-1, 2)\) is a solution. (1 point)
2. Determine whether \((3, -4)\) is a solution. (1 point)

Question 2: Line and shading (2 points)

For each inequality, state whether the boundary line is solid or dashed and whether the shading is above or below the line.

1. \(y<\frac{1}{2}x+2\) (1 point)
2. \(y\ge -x+1\) (1 point)

Question 3: Graph one inequality (2 points)

Graph \(y\ge 2x-4\) on the grid.

Question 4: Standard form (2 points)

Graph \(x+2y<4\) on the grid.

Question 5: Write from a graph (2 points)

Write the inequality represented by the graph.

Question 6: Graph a system (2 points)

Graph the system \(y>-x+1\) and \(y\le 2x-2\) on the grid. Show the solution region clearly.

Question 7: Read a system (2 points)

The graph shows the solution region of a system of three inequalities.

1. Write the system. (1 point)
2. Determine whether \((1, 2)\) and \((3, 2)\) are solutions. (1 point)

Question 8: Overlap or not (2 points)

1. Does the system \(y>2x+1\) and \(y<2x-3\) have a solution? Explain. (1 point)
2. Describe the solution set of the system \(y\ge 3\) and \(y\le 3\). (1 point)

Question 9: Bake sale goal (2 points)

Priya sells cupcakes for \(\$3\) each and brownies for \(\$2\) each. She wants to earn at least \(\$48\). Let \(x\) be cupcakes and \(y\) be brownies.

1. Write an inequality for her goal. (1 point)
2. Determine whether selling 10 cupcakes and 9 brownies reaches the goal. (1 point)

Question 10: Shirts and caps (2 points)

Jamal has at most \(\$24\) to spend. Shirts cost \(\$8\) each and caps cost \(\$6\) each. He wants at least 2 shirts. Let \(x\) be shirts and \(y\) be caps.

1. Write a system of inequalities for the situation. (1 point)
2. Determine whether buying 3 shirts and 1 cap is possible, and whether buying 2 shirts and 1 cap is possible. (1 point)

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