Maryland Math A.REI.C.7.a

MathGrades 9–12REASONING WITH EQUATIONS AND INEQUALITIES

The Standard

A.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = −3x and the circle x² + y² = 3.

Solve systems of equations comprised of various combinations of all algebraic and transcendental functions in two variables.

Maryland College and Career Ready Standards for Mathematics (2025) · Solve systems of equations.

Teacher's field guide

What Students Need to Do: Students find points where two graphs meet, even when the equations use different kinds of functions. They solve with algebra when they can, estimate from graphs when needed, and check each point in both equations.
What Mastery Looks Like: Given a line and a parabola, or a line and an exponential curve, students find every intersection in a stated domain. They report ordered pairs, label estimates, and reject values that make an equation undefined.
Common Misconceptions: Students may give only an x-value instead of an ordered pair. They may miss another crossing outside their graph window or keep a value that makes a denominator zero.
How to Assess It: Exit ticket: Graph y=2^x and y=x+2 for −3≤x≤4. Report every intersection as an ordered pair and check each in both equations.

Lesson moves

Trace y=x²−1 and y=x+1 on separate clear sheets, align the axes, and mark both crossings before checking each pair.
Have students sketch y=sin(x) and y=0 from −2π to 2π and explain why a narrower graph window misses answers.
Give pairs cards with y=x² and y=x+2, and y=2^x and y=x+2; race to match each system to its graph.
Graph a phone worth $600 losing 20% yearly and a repair bill starting at $150 and rising $20 yearly; estimate when they match.

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