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CCSS HSA-REI.C.6 Worksheets

Algebra 2 · Reasoning with Equations & Inequalities

Solve systems of linear equations exactly and approximately (e.g., with graphs). The standard focuses on pairs of equations in two variables; this Algebra 2 module extends it to systems of three linear equations in three variables solved by elimination.

Below are free printable worksheets that support HSA-REI.C.6. Print them as PDFs, or generate a fresh one. Every math answer key is computed in code, so it is never wrong.

Teaching guide

What students learn

Solve systems of linear equations exactly and approximately (e.g., with graphs). The standard focuses on pairs of equations in two variables; this Algebra 2 module extends it to systems of three linear equations in three variables solved by elimination.

Worked example
Solve the system: x + y + z = -12; 3x + y + 4z = -38; -4x - y + 2z = 6
Answer: x = -4, y = -2, z = -6
Why: By Cramer's rule, D = det of the coefficient matrix = -15. Replacing each column with the constants [-12, -38, 6] gives D_x = 60, D_y = 30, D_z = 90. Then x = D_x/D = 60/-15 = -4, y = D_y/D = 30/-15 = -2, z = D_z/D = 90/-15 = -6. Check in equation 1: (1)(-4) + (1)(-2) + (1)(-6) = -12.

Generated and checked in code, so it is correct.

Algebra worksheets

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Algebra 2 Algebra
Set A · PDF · answer key with Pro
Make a worksheet for HSA-REI.C.6
More Algebra 2 standards: HSF-IF.A.3 · HSF-BF.A.2 · HSA-SSE.B.4 · HSA-REI.C.7 · HSA-REI.C.8 · HSN-VM.C.7 · HSN-VM.C.8 · HSA-APR.D.6
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