8.EE.8: Solve Systems of Linear Equations
Also written as 8.EE.C.8 and CCSS.MATH.CONTENT.8.EE.C.8 · Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.
The Official Wording
Analyze and solve pairs of simultaneous linear equations.
Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 8.EE.8 Means in Plain English
Eighth graders learn that a system’s solution is the point on both lines: y = 2x + 1 and y = -x + 7 cross at (2, 5), which makes both true. They estimate by graphing, solve exactly by substitution, and see by inspection when lines never meet.
Part c puts systems to work: ticket sales, two phone plans, or whether lines through two pairs of points cross. In high school students solve systems exactly and approximately by any method (HSA-REI.6) and extend the idea to a line meeting a curve (HSA-REI.7).
8.EE.8 I Can Statements
- I can explain why the intersection point solves both equations.
- I can solve a system by graphing, substitution or inspection.
- I can write and solve a system from a word problem.
8.EE.8 Worked Example
A drama club ticket problem: two facts, two equations, and one point where both are true.
The drama club sold 120 tickets and took in $735. Adult tickets cost $8 and student tickets cost $5. How many of each did they sell?
- Name the unknowns and write one equation for each fact: one counts tickets, the other counts dollars.a + s = 120 and 8a + 5s = 735
- Solve the first equation for s and substitute into the second, so only one variable is left.s = 120 - a, so 8a + 5(120 - a) = 735
- Distribute and collect like terms.8a + 600 - 5a = 735, so 3a = 135
- Divide by 3, then go back to the first equation for s.a = 45, and s = 120 - 45 = 75
- On a graph, the two lines cross at exactly this point, the only pair that sits on both.Intersection: (45, 75)
Check it: Substitute into both equations: 45 + 75 = 120, and 8 × 45 + 5 × 75 = 360 + 375 = 735.
Common Mistakes with 8.EE.8
Stopping after one variable
“a = 45, done.”
Try this: Substitute the first value back to find the second, and answer the question asked: 45 adult and 75 student tickets.
Checking in one equation only
(50, 70) checked in a + s = 120 and accepted
Try this: Test the pair in both equations: 50 + 70 = 120, but 8 × 50 + 5 × 70 = 750, not 735.
Reading a false statement as an error
“x + y = 4 and x + y = 9 gave 4 = 9, so I made a mistake.”
Try this: Interpret the false statement: the lines are parallel, never cross, and the system has no solution at all.
Where 8.EE.8 Fits
Practice 8.EE.8
Quick Check
- Solve y = 3x - 2 and y = x + 4.
- How many solutions does the system y = 2x + 5 and y = 2x - 1 have?
- Twelve coins, all dimes and quarters, are worth $2.10. How many of each are there?