Elimination

Learn and apply elimination using equations, examples, and interpretation.

Lesson 3 of 53 parts Practice Flashcards

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Adding Equations

Objective: Explain and use adding equations in an Algebra 1 problem.

Add equations with aligned like terms so opposite coefficients cancel one variable while preserving the common solution. Coefficients of the same variables and constants.

Worked examples

Try itExample 1.1: Solve x+y=21 and x−y=-11. Find x.Show answer

5. Add the two equations so y cancels, then divide by two. The answer is 5.

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Adding Equations

Objective: Explain and use adding equations in an Algebra 1 problem.

Add equations with aligned like terms so opposite coefficients cancel one variable while preserving the common solution. Coefficients of the same variables and constants.

Worked examples

Try itExample 1.1: Solve x+y=21 and x−y=-11. Find x.Show answer

5. Add the two equations so y cancels, then divide by two. The answer is 5.

Scaling Before Elimination

Objective: Explain and use scaling before elimination in an Algebra 1 problem.

Multiply an entire equation by a nonzero constant to create opposite coefficients, then add the equations. Partial scaling would change its solutions.

Worked examples

Try itExample 2.1: Solve x+y=34 and x−y=-18. Find x.Show answer

8. Add the two equations so y cancels, then divide by two. The answer is 8.

Solution Verification

Objective: Explain and use solution verification in an Algebra 1 problem.

After elimination and back-substitution, check the ordered pair in both original equations. An arithmetic error or invalid candidate.

Worked examples

Try itExample 3.1: Solve x+y=47 and x−y=-25. Find x.Show answer

11. Add the two equations so y cancels, then divide by two. The answer is 11.

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