Wyoming Math 8.EE.8c
The Standard
Analyze and solve pairs of simultaneous linear equations. Solve simple real-world and mathematical problems leading to two linear equations in two variables given y = mx + b form with integer solutions.
2023 Wyoming Mathematics Content and Performance Standards · Analyze and solve linear equations and pairs of simultaneous linear equations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve two equations in y = mx + b form by graphing or setting the expressions for y equal. They write the shared point as an ordered pair and explain what it means in a word problem.
What Mastery Looks Like
- Given y = 2x + 5 and y = 3x + 1, a student finds (4, 13) and checks it in both equations. In a rental problem, they explain that the plans cost the same after 4 hours, at $13.
Common Misconceptions
- Students may treat a starting fee as an hourly rate. They may give only the x-value instead of the ordered pair, or check their answer in just one equation.
How to Assess It
- Exit ticket: Two gyms charge y = 3x + 2 and y = x + 10 dollars for x visits. Find when the prices match, state the cost, and check your point in both equations.
Lesson moves
Ways to Teach It
Build two counter stacks, starting at 5 and 1; add 2 and 3 each round, then record when the stacks match.
Ask students to explain why (4, 13) solves both y = 2x + 5 and y = 3x + 1, but (3, 11) does not.
Put y = 2x + 1 and y = x + 4 on the board; partners race to find and verify the shared point.
Post two bike-rental signs, $5 plus $2 per hour and $1 plus $3 per hour; ask when the costs match.
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Printable 8.EE.8c Worksheet
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Related Standards
- 8.EE.8b
Solve systems of two linear equations in two variables with integer solutions by graphing the equations.
- 7.EE.4a
Write and fluently solve linear equations of the form ax +b = c and a(x + b) = c where a, b, and c are rational numbers.
- 6.EE.7
Write and solve real-world and mathematical problems in the form of one-step, linear equations involving non negative rational numbers.
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