8th Grade Systems of Linear Equations Test Solutions and Scoring (PDF)
This systems of equations test answers for 8th Grade covers systems of linear equations (Common Core 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c), with a free PDF to print.
Use this answer key to score the systems of linear equations test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.
Grade 8 · Common Core State Standards: 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c
Systems of equations test answers: worked solutions
Question 1 – Check [2 pts]
\(4 + 2 = 6\) is true. \(12 – 1 = 11\) is true.
Yes
Scoring: 1 point for each equation checked.
Question 2 – Graph [3 pts]
Check: \(3 = 3\) and \(3 = -3 + 6\).
Scoring: 1 point for the point, 2 points for the check.
Question 3 – Substitution [3 pts]
\(3x + 2x + 1 = 16\), so \(5x = 15\) and \(x = 3\).
\(y = 2 \cdot 3 + 1 = 7\).
\((3, 7)\)
Scoring: 1 point for substituting, 1 point for x, 1 point for y.
Question 4 – Elimination [3 pts]
Add: \(6x = 24\), so \(x = 4\).
\(16 + y = 17\), so \(y = 1\).
\((4, 1)\)
Scoring: 1 point for adding, 1 point for x, 1 point for y.
Question 5 – Number of solutions [3 pts]
- No solution.
- Both lines have slope \(\frac{1}{2}\), but the intercepts are 1 and 4. They are parallel.
Scoring: 1 point for no solution. 1 point for equal slopes. 1 point for different intercepts.
Question 6 – Tickets [3 pts]
\(a + s = 7\) and \(12a + 8s = 68\). Then \(12a + 56 – 8a = 68\), so \(4a = 12\) and \(a = 3\).
3 adult and 4 student tickets
Scoring: 1 point for the system, 1 point for solving, 1 point for both answers.
Question 7 – Boat [2 pts]
\(b + c = 9\) and \(b – c = 5\). Subtract: \(2c = 4\), so \(c = 2\).
2 miles per hour
Scoring: 1 point for the system. 1 point for 2 mph.
Question 8 – Explain [1 pt]
The intersection point lies on both lines, so its coordinates satisfy both equations.
Scoring: 1 point for a correct explanation.
Total score
20 points
Key facts behind this systems of equations test answers
- The solution of a system is the intersection point of the lines.
- Different slopes: one solution. Same slope, different intercepts: no solution. Same line: infinitely many.
- Substitution: solve one equation for a variable and substitute it into the other.
- Elimination: add or subtract the equations to cancel a variable.
- Always check the ordered pair in both equations.
How to use this systems of equations test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Grade 8 chapters: Grade 8 math.
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