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Cogito

Integrated Math 1 · Chapter 3 · Lesson 2

Practice Worksheet

Solving Systems by Elimination

Add the equations and lose a variable.

12 problems · about 21 minutes · A-REI.C.5, A-REI.C.6

NameDate

Figure — use these to answer the problems

Two lines meeting at one point. Elimination finds that point without drawing anything.
-10-10-5-5551010
y = -2x + 6
Slope-2
y-intercept6
Point x2
Point y2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. x + y = 12 and x − y = 2. What is x?

    Answer

  2. Why may an equation be multiplied by a constant?

    • Scaling both sides equally leaves the same solutions.
    • It makes the numbers smaller.

  3. x + y = 10 and x − y = 4. What is x?

    Answer

  4. Same system. What is y?

    Answer

  5. 3x + y = 10 and 2x − y = 5. What is x?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 2x + 2y = 14 and x − y = 1. What is x?

    Answer

  2. To eliminate from 2x and 3x, what common multiple do you scale to?

    Answer

  3. Does multiplying an equation throughout change its solutions? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each system by the better first method.

    Write each item under the heading it belongs to: y = 3x + 2 and 2x + y = 12 · x = 5 − y and 3x + y = 11 · 2x + 3y = 12 and 4x − 3y = 6 · 5x + 2y = 9 and 3x − 2y = 7

    Substitution

    Elimination

  2. 4x + y = 14 and 2x − y = 4. What is x?

    Answer

  3. The Cancellation

    2x + 3y = 12 and 4x − 3y = 6. What is x?

    Answer

  4. The Second Value

    Same system. What is y?

    Answer