Algebra 1 Systems of Linear Equations Test with Point Values (PDF)

Algebra 1 math test: Systems of Linear Equations – Maths PDF

This systems test for Algebra 1 covers systems of linear equations (Common Core A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3), with a free PDF to print.

Systems test (Algebra 1) – first page of the printable PDF
This 45-minute test on systems of linear equations covers Common Core A-REI.C.5, A-REI.C.6, and A-REI.D.11 and is worth 20 points. Work alone, show all steps, and use a calculator only if your teacher allows it. Partial credit is given for correct work, so write down your reasoning even when you are unsure of the final answer.

Time and points

About this test
  • Grade: Algebra 1
  • Chapter: Systems of Linear Equations
  • Standards: A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3
  • Time: 45 minutes
  • Total: 20 points

Systems test: questions

Question 1 – Check a solution [2 pts]

Is \((3, -1)\) a solution of the system \(x + 2y = 1\) and \(3x – y = 10\)? Show your work.

Question 2 – Solve by graphing [2 pts]

xy-2-1123456-4-3-2-112345
Grid for question 2.

Solve by graphing: \(y = 2x – 2\) and \(y = -x + 4\).

Question 3 – Substitution [2 pts]

Solve by substitution: \(y = 2x – 3\) and \(3x + y = 12\).

Question 4 – Elimination [2 pts]

Solve by elimination: \(4x + 3y = 17\) and \(2x – 3y = -5\).

Question 5 – Elimination with multiplying [2 pts]

Solve: \(3x + 2y = 7\) and \(2x – 5y = -8\).

Question 6 – Number of solutions [2 pts]

Describe the number of solutions of each system.

  1. \(y = -2x + 3\) and \(4x + 2y = 6\) (1 point)
  2. \(y = x + 1\) and \(y = x + 4\) (1 point)

Question 7 – Ticket sales [3 pts]

TicketPriceStudent$5Adult$8
Ticket prices.

A school play sold 150 tickets. Student tickets cost $5 and adult tickets cost $8. The total sales were $930. Let \(s\) be the student tickets and \(a\) the adult tickets.

  1. Write a system of equations. (1 point)
  2. Solve the system. (1 point)
  3. Check your answer. (1 point)

Question 8 – Break-even point [3 pts]

xy51015202530100200300400500(20, 300)
Cost and revenue of a lawn business (x in lawns).

A lawn business has costs \(y = 200 + 5x\) and revenue \(y = 15x\) dollars for \(x\) lawns. The graph shows both lines.

  1. Write an equation to find when cost equals revenue. (1 point)
  2. Solve it. (1 point)
  3. Explain the meaning of the intersection point. (1 point)

Question 9 – Find the error [2 pts]

A student says \((4, 6)\) is the solution of \(x + y = 10\) and \(x – y = 2\). Show that this is wrong and find the correct solution.

View solution

Key facts behind this systems test

Key facts
  • A solution of a system is an ordered pair that satisfies every equation.
  • Graphing: the solution is the intersection point of the lines.
  • Substitution: solve one equation for a variable and substitute into the other.
  • Elimination: add or subtract equations to cancel a variable.
  • Parallel lines give no solution; identical lines give infinitely many.

How to use this systems 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.

Prepare for the test

All Algebra 1 chapters: Algebra 1 math.

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