Montana Math MT.CORE.ALG.LIN.6
The Standard
Solve systems of linear equations by graphing, substitution, and elimination, including systems with zero, one, or infinite solutions, while using technology and representations strategically.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find values that make both equations true by graphing, substitution, or elimination. They decide whether the lines meet once, never meet, or match exactly. They use a graphing app to estimate intersections, then check their answers in both equations.
What Mastery Looks Like
- Students choose substitution when a variable is isolated and elimination when coefficients line up. They verify an intersection in both equations. They recognize that 0=5 means no solution and 0=0 means infinitely many solutions.
Common Misconceptions
- Students may treat a point read from a graph as exact, even when it falls between grid marks. After elimination, they may try to divide by zero instead of interpreting 0=5 or 0=0. They may check an answer in only one equation.
How to Assess It
- Exit ticket: Classify these systems as having one, no, or infinitely many solutions: x+y=4 and x−y=2; x+y=4 and 2x+2y=8; x+y=4 and x+y=5. Solve the first by elimination and explain the other two with a sketch or algebra.
Lesson moves
Ways to Teach It
On graph paper, draw x+y=4, 2x+2y=8, and x+y=5 in different colors; trace overlapping lines and mark parallel ones.
Ask pairs why subtracting x+y=4 from x+y=5 gives 0=1, and what that says about the lines.
Give partners two cards, x+y=6 with x−y=2, and y=2x+1 with x+y=7; solve the first by elimination and second by substitution.
Enter bike rental costs, $10 plus $3 per hour and $4 plus $5 per hour, in a graphing app to find equal costs.
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Printable MT.CORE.ALG.LIN.6 Worksheet
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