This algebra 1 systems test answer key gives the full solution and the scoring guide for each of the 10 test questions on systems of linear equations.
Use this key to score the test out of 20 points. Each solution shows a full method and a scoring guide, so partial credit can be given when the setup is right but an arithmetic slip changes the final answer. Accept any valid method unless the question names one.
Algebra 1 Systems Test Answer Key: questions 1–5
Question 1: Is it a solution? (2 points)
- \(2(4)+(-1)=7\) and \(4-3(-1)=7\). Both true: yes.
- \(2(3)+1=7\) is true, but \(3-3(1)=0\neq 7\). No.
Scoring: 1 point for each part, with both equations checked in each.
Question 2: Read the solution (2 points)
- The lines cross at \((2, 2)\).
- \(-2+4=2\) and \(\frac{1}{2}(2)+1=2\). Both are true.
Scoring: 1 point for the point, 1 point for checking both equations.
Question 3: Solve by graphing (2 points)
Line 1 passes through \((0, -1)\) and \((2, 1)\). Line 2 passes through \((0, 5)\) and \((2, 1)\). They cross at \((2, 1)\).
Scoring: 1 point for both lines graphed correctly, 1 point for the solution.
Question 4: Substitution (2 points)
Substitute: \(3x+2(4x-7)=8\), so \(11x-14=8\) and \(x=2\). Then \(y=4(2)-7=1\).
Check: \(3(2)+2(1)=8\).
The solution is \((2, 1)\).
Scoring: 1 point for \(x=2\), 1 point for \(y=1\).
Question 5: Opposite coefficients (2 points)
Add the equations: \(7x=-14\), so \(x=-2\). Then \(5(-2)+3y=-1\) gives \(3y=9\) and \(y=3\).
Check: \(2(-2)-3(3)=-13\).
The solution is \((-2, 3)\).
Scoring: 1 point for \(x=-2\), 1 point for \(y=3\).
Algebra 1 Systems Test Answer Key: questions 6–10
Question 6: Multiply first (2 points)
Multiply the first equation by \(3\) and the second by \(2\): \(9x+6y=30\) and \(10x+6y=34\).
Subtract: \(x=4\). Then \(12+2y=10\) gives \(y=-1\).
Check: \(5(4)+3(-1)=17\).
The solution is \((4, -1)\).
Scoring: 1 point for a correct elimination setup with \(x=4\), 1 point for \(y=-1\).
Question 7: Count the solutions (2 points)
- \(6x+2y=4\) gives \(y=-3x+2\), the same line. Infinitely many solutions.
- \(4x-2y=6\) gives \(y=2x-3\). The slopes are equal (\(2\)) and the intercepts differ (\(-3\) and \(5\)). No solution.
Scoring: 1 point per part, for the correct count with a valid reason.
Question 8: Explain elimination (2 points)
- A solution makes \(3x+y=11\) and \(2x-y=4\) both true. Adding equal amounts to both sides of equations keeps them true, so the sum \(5x=15\) is also true for that pair.
- \(x=3\). Then \(3(3)+y=11\) gives \(y=2\). Check: \(2(3)-2=4\). The solution is \((3, 2)\).
Scoring: 1 point for an explanation based on equal quantities added to equal quantities, 1 point for \((3, 2)\).
Question 9: Ticket problem (2 points)
Let \(s\) be student tickets and \(a\) adult tickets: \(s+a=150\) and \(6s+10a=1100\).
Substitute \(s=150-a\): \(900-6a+10a=1100\), so \(4a=200\) and \(a=50\). Then \(s=100\).
Check: \(6(100)+10(50)=1100\).
100 student tickets and 50 adult tickets.
Scoring: 1 point for a correct system, 1 point for the two answers.
Question 10: Gym memberships (2 points)
- Gym A: \(C=20m+30\). Gym B: \(C=35m\).
- \(20m+30=35m\), so \(30=15m\) and \(m=2\). Cost: \(35(2)=70\), and \(20(2)+30=70\). After 2 months, both cost \(\$70\).
Scoring: 1 point for both equations, 1 point for \(m=2\) and \(\$70\).
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 Systems of Linear Equations test answer key
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