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Cogito

Grade 8 Math · Chapter 5 · Lesson 2

Practice Worksheet

Solving a System by Substitution

Replace one letter and one equation is left.

10 problems · about 20 minutes · 8.EE.C.8

NameDate

Figure — use these to answer the problems

The solution of a system is the point where the two lines cross.
-10-10-5-5551010
y = 2x + 1
Slope2
Intercept1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Where Two Lines Meet”

    y = 5x and y = 3x + 8. What is x?

    Answer

  2. From “Writing Equations from Situations”

    6 + 5m = 3m + 20. What is m?

    Answer

  3. From “Equations with Brackets and Fractions”

    5(x + 1) = 40. What is x?

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. y = 4x and x + y = 15. What is x?

    Answer

  2. y = x + 2 and x + y = 10. What is x?

    Answer

  3. Same system. What is y?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. y = 2x and 3x + y = 20. What is x?

    Answer

  2. Does a solution have to satisfy both equations? 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

2 problems

  1. The Substitution

    y = 3x and x + y = 12. What is x?

    Answer

  2. The Other Half

    Same system. What is y?

    Answer