Ten multiple-choice questions check your skill with systems of linear equations: reading intersections, testing ordered pairs, substitution, elimination, no-solution systems and word problems. Choose the one correct answer, then read the explanation to learn from any mistake.
Grade 8Common Core: 8.EE.C.8a · 8.EE.C.8b · 8.EE.C.8c
🎯 Systems of Linear Equations – Grade 8 math quiz
Question 1
The graph shows the system \(y=x+1\) and \(y=-x+5\). What is the solution?The lines cross at point A.
A
\((3,2)\)
B
\((2,3)\)
C
\((0,1)\)
D
\((0,5)\)
Question 2
Which ordered pair satisfies both \(y=3x+1\) and \(x+y=5\)?
A
\((1,4)\)
B
\((0,1)\)
C
\((2,3)\)
D
\((4,1)\)
Question 3
Solve by substitution: \(y=x+3\) and \(2x+y=12\).
A
\((6,3)\)
B
\((3,9)\)
C
\((3,6)\)
D
\((4.5,7.5)\)
Question 4
Solve by elimination: \(x+y=9\) and \(x-y=1\).
A
\((4,5)\)
B
\((5,4)\)
C
\((8,1)\)
D
\((10,-1)\)
Question 5
Which system has no solution?
A
\(y=3x+1\) and \(y=-3x+1\)
B
\(y=3x+1\) and \(y=3x-4\)
C
\(y=3x+1\) and \(6x-2y=-2\)
D
\(y=3x+1\) and \(y=\frac{1}{3}x+1\)
Question 6
How many solutions does \(y=2x+5\) and \(4x-2y=-10\) have?
A
No solution
B
Exactly one
C
Infinitely many
D
Exactly two
Question 7
Two numbers have a sum of 20 and a difference of 4. What are the numbers?The two equations for the numbers.
A
10 and 10
B
16 and 4
C
14 and 6
D
12 and 8
Question 8
Sofia buys 2 sandwiches and 1 juice for $11. Ethan buys 1 sandwich and 1 juice for $7. What does one sandwich cost?
A
$3 for a sandwich, $4 for a juice
B
$5 for a sandwich, $2 for a juice
C
$2 for a sandwich, $5 for a juice
D
$4 for a sandwich, $3 for a juice
Question 9
The graphs of two equations cross at \((3,5)\). What does this mean?The graphs meet at \((3,5)\).
A
\(x=3\) and \(y=5\) make both equations true
B
\(x=5\) and \(y=3\) make both equations true
C
\(x=3\) and \(y=5\) make only one equation true
D
The two equations have no solution
Question 10
Which equation can be paired with \(2x+y=8\) so the solution is \((3,2)\)?
A
\(x-y=-1\)
B
\(x+y=6\)
C
\(x-y=1\)
D
\(2x-y=3\)
🎉 Quiz complete!
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Remember:
- Standards 8.EE.C.8a, 8.EE.C.8b and 8.EE.C.8c: solve systems of two linear equations in two variables and use them in real-world problems.
- The solution of a system is the point where the two graphs intersect.
- Substitution replaces one variable with an expression; elimination adds or subtracts equations to cancel a variable.
- Parallel lines (same slope, different intercepts) mean no solution; the same line twice means infinitely many.
- Always check the ordered pair in both original equations.
See every chapter on the Grade 8 math page.