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Cogito

Algebra 1 · Chapter 5 · Lesson 3

Practice Worksheet

Systems in Context

Two unknowns, two conditions.

11 problems · about 23 minutes · A-CED.A.3

NameDate

Figure — use these to answer the problems

Two groups making one total is the first equation of most systems.
adult and child
all tickets
Adult tickets6
Child tickets9
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

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

    Answer

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

    Answer

  3. Same system. What is y?

    Answer

  4. How many equations are needed for two unknowns?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 2x + y = 12 and y = 4. What is x?

    Answer

  2. 20 coins are 5p and 10p, worth 150p. If there are 10 tens, how many fives?

    Answer

  3. Order the steps for a system word problem.

    Write 1 to 4 in the boxes to put these in order.

    • Name both unknowns
    • Write one equation per condition
    • Solve the system
    • Answer in the words of the problem

Stretch Yourself

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

4 problems

  1. x + y = 9 and x = 2y. What is y?

    Answer

  2. Same system. What is x?

    Answer

  3. The Count

    a + c = 15 and a = 7. What is c?

    Answer

  4. The Money

    7 adults at £8 each. How much, in pounds?

    Answer