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Systems Checkpoint

A free Algebra I lesson from the “Systems of Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint tests whether you can choose a systems strategy. Some systems are easiest by substitution, some by elimination, and word problems require translating two relationships first.

What you'll learn

Why it matters: Systems checkpoints mirror real planning questions where two conditions must be true at once, such as matching costs while meeting a quantity requirement.

Worked example

Problem. Solve y = x + 4 and x + y = 16.

  1. Substitute x + 4 for y in x + y = 16.
  2. x + x + 4 = 16, so 2x = 12 and x = 6.
  3. y = 6 + 4 = 10.

Answer: (6, 10)

Practice problems

1. The solution to a graphed system is the...

Choices: Intersection point · steepest line · x-axis label · larger intercept

Show solution
  1. Graphing Systems: First identify exactly what the question is asking: The solution to a graphed system is the...
  2. For a system, use substitution, elimination, or graphing to find the value pair that makes both equations true.
  3. Both equations are true where the lines meet.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Intersection point

2. Solve y = x + 1 and x + y = 11. Enter x.

Show solution
  1. Substitution: First identify exactly what the question is asking: Solve y = x + 1 and x + y = 11. Enter x.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x + 1 for y.
  4. 2x + 1 = 11, so x = 5.
  5. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

3. For y = x + 1 and x + y = 11, enter y.

Show solution
  1. Substitution: First identify exactly what the question is asking: For y = x + 1 and x + y = 11, enter y.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Use x = 5.
  4. y = 6.
  5. Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.

Answer: 6

4. Solve y = 3x - 2 and y = 10. Enter x.

Show solution
  1. Substitution: First identify exactly what the question is asking: Solve y = 3x - 2 and y = 10. Enter x.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Set 3x - 2 = 10.
  4. 3x = 12, so x = 4.
  5. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

5. Solve x + y = 13 and x - y = 3. Enter x.

Show solution
  1. Elimination: First identify exactly what the question is asking: Solve x + y = 13 and x - y = 3. Enter x.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add the equations: 2x = 16.
  4. x = 8.
  5. Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.

Answer: 8

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