Home/Integrated Math 1/Lesson 84

Solve a system of equations using elimination

Eliminate one variable by combining equations strategically.

Do this: Read the concept below, then try the quiz or activity.

Lesson 84 of 192

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Concept

Objective: Students will solve systems using elimination and justify each operation.

Estimated Time: 12 minutes

Standards:

HSA-REI.C.6HSA-CED.A.3

Multiply equations when needed so one variable has opposite coefficients, then add/subtract to eliminate it.

Try it

Solve 2x + y = 9 and 2x - y = 3.

⚖️ System Solver (2x2)

Practice elimination and verify with a system solver.

Equation 1

2x + 1y = 9

Equation 2

1x - 1y = 1

Determinant: D = ae - bd = (2)(-1) - (1)(1) = -3
x = (ce - bf) / D = (9-1 - 1+1) / -3 = 3.333
y = (af - cd) / D = (2+1 - 9+1) / -3 = 2.333

Solution: (3.333, 2.333)

Concept Check

In elimination, why multiply an equation first?

To change solution set

To create opposite coefficients

To remove constants

To force graphing

Concept Check

After elimination gives x, what next?

Guess y

Back-substitute for y

Restart

Ignore y

Common Misconception

Always verify your result in context instead of trusting a first pass.

Elimination method flow

These steps are out of order — can you fix them?

1.Back-substitute and verify

2.Add/subtract to eliminate

3.Create opposite coefficients

4.Align equations

Short Answer

What is a common elimination mistake?

Mastery Check

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Question 1