Algebra 1 Linear Inequalities in Two Variables and Systems Test Solutions and Scoring (PDF)

a) \(1 \le -1 + 3 = 2\) true: yes.

b) \(1 \le -3 + 3 = 0\) false: no.

Scoring: 1 point for each part.

The symbol > is strict, so the line is dashed. Since \(y\) is greater than the expression, shade above the line.

Dashed; shade above

Scoring: 1 point for the line type; 1 point for the shaded side.

Graph the solid line through \((0, 1)\) with slope \(\frac{1}{2}\). Shade above.

Scoring: 1 point for the correct solid line; 1 point for shading the correct side.

Subtract \(2x\): \(-y < -2x + 4\). Divide by \(-1\) and reverse the symbol: \(y > 2x – 4\).

\(y > 2x – 4\); dashed line through (0, -4) with slope 2, shade above

Scoring: 1 point for reversing the symbol correctly; 1 point for the description.

The solid line passes through \((0, 2)\) with slope \(-1\), so it is \(y = -x + 2\). Shading is below, and the line is solid.

\(y \le -x + 2\)

Scoring: 1 point for the boundary line; 1 point for the correct symbol.

First: \(3 > 2\) true. Second: \(3 \le -2 + 6 = 4\) true.

Yes

Scoring: 1 point for each inequality checked.

The boundary \(y = x – 2\) is solid with shading above. The boundary \(y = -x + 4\) is dashed with shading below.

The lines meet where \(x – 2 = -x + 4\): \(x = 3\), \(y = 1\).

Overlap region with corner \((3, 1)\)

Scoring: 1 point for each correct boundary and shading; 1 point for the corner.

a) \(4x + 3y \ge 80\).

b) \(4(10) + 3(15) = 85 \ge 80\), so yes.

c) \(4(8) + 3(12) = 68 \ge 80\) is false, so no.

\(4x + 3y \ge 80\); yes; no

Scoring: 1 point per part.

\(x \ge 2\), \(y \ge 1\), \(x + y \le 10\).

One solution is \((4, 3)\): \(4 \ge 2\), \(3 \ge 1\), \(7 \le 10\).

System above; for example (4, 3)

Scoring: 1 point for the system; 1 point for a valid solution.