Montana Math MT.CORE.ALG.LIN.5

MathGrades 9–12Linear Functions and Expressions

The Standard

Understand that a solution to a system of equations is a coordinate pair that makes both equations true.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students substitute the x and y values of a coordinate pair into each equation. They explain why the pair is a solution only if both equations are true.
What Mastery Looks Like: Given x+y=7 and y=2x+1, a student identifies (2,5) and shows that it makes both equations true. On a graph, they find the same pair where the lines cross.
Common Misconceptions: Students may stop checking after the pair works in one equation. They may swap x and y, or think any point on either line solves the system.
How to Assess It: Exit ticket: Does (3,4) solve x+y=7 and y=2x+1? Show both checks and explain your answer.

Lesson moves

On a floor grid, use yarn to trace y=x+1 and y=-x+5, then label their shared point and check it in both equations.
For x+y=7 and y=2x+1, ask students to explain why (3,4) fails even though it satisfies one equation.
Deal cards with (2,5), (3,4), and (1,6); students race to find which solves x+y=7 and y=2x+1.
Present ten tickets costing $65, with adult tickets at $8 and child tickets at $5; check whether (5,5) fits both facts.

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