NY Next Generation Math NY-8.EE.8.b

Math8th GradeAnalyze and solve pairs of simultaneous linear equations.

The Standard

Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students fluently solve two-variable systems with integer coefficients by graphing, tables, substitution, elimination, and inspection. Algebraic tasks include at least one equation with a variable coefficient of 1.

What Mastery Looks Like

A student solves y = 2x + 1 and y = -x + 7 by substitution to get x = 2 and y = 5. The student confirms (2, 5) graphically or in a table and checks both equations.

Common Misconceptions

Students may combine equations without preserving equality or stop after finding one coordinate. They may read a graph's crossing point without verifying it or overlook a system solvable by inspection.

How to Assess It

Give students y = x + 4 and 2x + y = 10. Ask them to solve algebraically and with a table or graph, then verify the ordered pair.

Lesson moves

Ways to Teach It

  1. Solve one integer-coefficient system with graph paper, value tables, substitution, and elimination, comparing the shared result.

  2. Ask students which feature of a system makes inspection, substitution, or elimination efficient.

  3. Play systems method choice with equation pairs, proposed methods, solution steps, and verification cards.

  4. Find when two integer-rate plans have the same total using two solution methods.

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