This algebra 1 systems test answer key gives the full solution and the scoring guide for each of the 10 test questions on graphing linear inequalities and systems of inequalities.
Use this key to score the test out of 20 points. Each solution shows the graph or reasoning and a scoring guide, so partial credit can be given when the boundary is right but the shading is not. Accept any equivalent form of an inequality.
Algebra 1 Systems Test Answer Key: questions 1–5
Question 1: Test two points (2 points)
- \(2>2(-1)-3=-5\) is true. Yes.
- \(-4>2(3)-3=3\) is false. No.
Scoring: 1 point per part for the substitution and the correct conclusion.
Question 2: Line and shading (2 points)
- Dashed line, shaded below.
- Solid line, shaded above.
Scoring: 1 point per part; both the line type and the shading side must be correct.
Question 3: Graph one inequality (2 points)
The boundary passes through \((0, -4)\) and \((2, 0)\) and is solid. Test \((0, 0)\): \(0\ge -4\) is true, so shade the side with the origin, above the line.
Scoring: 1 point for the correct solid boundary, 1 point for shading the correct side.
Question 4: Standard form (2 points)
The intercepts are \((4, 0)\) and \((0, 2)\). The boundary is dashed. Test \((0, 0)\): \(0<4\) is true, so shade the side containing the origin.
Scoring: 1 point for the dashed boundary through both intercepts, 1 point for correct shading.
Question 5: Write from a graph (2 points)
The line passes through \((0, 1)\) and \((2, 2)\), so its slope is \(\frac{1}{2}\) and its equation is \(y=\frac{1}{2}x+1\). The line is solid and the shading is below it.
The inequality is \(y\le \frac{1}{2}x+1\).
Scoring: 1 point for the boundary equation, 1 point for the correct symbol.
Algebra 1 Systems Test Answer Key: questions 6–10
Question 6: Graph a system (2 points)
\(y=-x+1\) is dashed with shading above. \(y=2x-2\) is solid with shading below. They meet where \(-x+1=2x-2\), so \(x=1\) and \(y=0\). The point \((1, 0)\) is not a solution, because \(0>0\) is false.
Scoring: 1 point for both boundary lines with the correct line types, 1 point for the correct overlapping region.
Question 7: Read a system (2 points)
- The bottom edge is solid with shading above: \(y\ge 1\). The left edge is solid with shading to the right: \(x\ge -1\). The slanted edge \(y=-x+4\) is dashed with shading below: \(y<-x+4\).
- \((1, 2)\): \(2\ge 1\), \(1\ge -1\) and \(2<3\) are true, so yes. \((3, 2)\): \(2<1\) is false, so no.
Scoring: 1 point for all three inequalities correct, 1 point for both decisions.
Question 8: Overlap or not (2 points)
- A solution would need \(2x+1<y<2x-3\), so \(2x+1<2x-3\), which gives \(1<-3\). That is false, so there is no solution: the lines are parallel and the regions do not overlap.
- Both conditions hold only when \(y=3\). The solution set is the horizontal line \(y=3\).
Scoring: 1 point per part for the correct conclusion with a valid reason.
Question 9: Bake sale goal (2 points)
- \(3x+2y\ge 48\)
- \(3(10)+2(9)=30+18=48\), and \(48\ge 48\) is true. Yes, the goal is reached.
Scoring: 1 point for each part.
Question 10: Shirts and caps (2 points)
- \(8x+6y\le 24\), \(x\ge 2\) and \(y\ge 0\).
- 3 shirts and 1 cap: \(8(3)+6(1)=30>24\). Not possible. 2 shirts and 1 cap: \(16+6=22\le 24\) and \(2\ge 2\). Possible.
Scoring: 1 point for the cost inequality and the shirt minimum, 1 point for both decisions.
Scoring summary
20 points: add the points of every question of this algebra 1 systems test answer key.
How to use this algebra 1 systems test answer key
Use this algebra 1 systems test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Algebra 1 Graphing Linear Inequalities and Systems of Inequalities test answer key
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