8th Grade Systems of Linear Equations Test with Point Values (PDF)

8th Grade math test: Systems of Linear Equations – Maths PDF

Cover of the book Grade 8 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 8 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This systems of equations test 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.

This 20-point test checks systems of two linear equations solved by graphing, substitution and elimination (Common Core 8.EE.C.8a, 8.EE.C.8b and 8.EE.C.8c). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Systems of Linear Equations
Standards: 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c
Time: 45 minutes
Total: 20 points

Systems of equations test: questions

Question 1 – Check [2 pts]

Is $(4, 1)$ a solution of $x + 2y = 6$ and $3x – y = 11$? Show your check.

Question 2 – Graph [3 pts]

A: y = x and B: y = -x + 6.

The graph shows $y = x$ and $y = -x + 6$. Find the solution and check it.

Question 3 – Substitution [3 pts]

Solve by substitution: $y = 2x + 1$ and $3x + y = 16$.

Question 4 – Elimination [3 pts]

Solve by elimination: $4x + y = 17$ and $2x – y = 7$.

Question 5 – Number of solutions [3 pts]

Lines A and B.

How many solutions does the system graphed have? (1 point)
Explain using slopes and intercepts. (2 points)

Question 6 – Tickets [3 pts]

Prices for the school play.

Adult tickets cost \$12 and student tickets cost \$8. Sofia buys 7 tickets for \$68. Write a system and find how many of each she bought.

Question 7 – Boat [2 pts]

A kayaker paddles 9 miles per hour downstream and 5 miles per hour upstream. Find the speed of the current.

Question 8 – Explain [1 pt]

Explain why the solution of a system is the point where the graphs intersect.

Key facts behind this systems of equations test

Key facts

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

Voter.. post

Free printable PDF