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MA.8.AR.4.2 · Algebraic Reasoning

How Many Solutions a Graphed System Has: Sample FAST Questions

A graphed system of two lines has one solution when the lines cross, no solution when they are parallel, and infinitely many when they sit on top of each other. 8th graders read the graph and name which case it is.

How the FAST tests this benchmark

On the FAST, students answer multiple choice and drop-down items about the number of solutions. Parallel lines are the case students miss most, because a graph window can make it look like two lines will meet somewhere off screen.

Skills students need

  • Read one solution from an intersection point
  • Recognize parallel lines as no solution
  • Recognize coinciding lines as infinitely many solutions
  • Connect slope and y-intercept to the number of solutions

Try 6 real MA.8.AR.4.2 questions

These come straight from Algebro's 8th grade pre-algebra question bank, easiest first. Answer one, check it, then move to the next.

Question 1 of 6

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Question 1EasyEquation Editor
Write a second linear equation in slope-intercept form so that the system with y=12x+3y = \frac{1}{2}x + 3 has infinitely many solutions.

Enter the full expression. If it has a variable, include it.

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More 8th grade algebraic reasoning benchmarks

MA.8.AR.4.3

Solving Systems of Equations by Graphing

MA.8.AR.1.1

Laws of Exponents with Variable Expressions

MA.8.AR.1.2

Multiplying Linear Expressions

MA.8.AR.4.2: Number of Solutions Practice | Algebro