Algebra 1 Linear Inequalities in Two Variables and Systems Test with Point Values (PDF)

Is each point a solution of \(y \le -x + 3\)?

1. \((1, 1)\) (1 point)
2. \((3, 1)\) (1 point)

For the inequality \(y > 2x – 4\), state whether the boundary line is solid or dashed and which side of the line is shaded.

Graph \(y \ge \frac{1}{2}x + 1\) on the grid.

Rewrite \(2x – y < 4\) in slope-intercept form and describe its graph.

Write the inequality graphed.

Is \((2, 3)\) a solution of the system \(y > x\) and \(y \le -x + 6\)? Show your work.

Graph the system \(y \ge x – 2\) and \(y < -x + 4\). Mark the corner of the solution region.

At a lemonade stand, large cups cost $4 (\(x\)) and small cups cost $3 (\(y\)). The goal is at least $80 in sales.

1. Write an inequality. (1 point)
2. Is selling 10 large and 15 small cups enough? (1 point)
3. Is selling 8 large and 12 small cups enough? (1 point)

Noah spends \(x\) hours on soccer and \(y\) hours on chess each week. He spends at least 2 hours on soccer, at least 1 hour on chess, and at most 10 hours in total. Write a system of inequalities and give one possible pair \((x, y)\).