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Cogito

Integrated Math 1 · Chapter 3 · Lesson 1

Practice Worksheet

Solving Systems by Graphing and Substitution

Where two conditions meet.

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

NameDate

Figure — use these to answer the problems

Change the slope and intercept. Parallel lines never meet, which is a system with no solution.
-10-10-5-5551010
y = x + 2
Slope1
y-intercept2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y = 2x and y = x + 5. What is x?

    Answer

  2. What does a solution to a system mean graphically?

    • The point where the lines cross.
    • Where each line meets the y-axis.

  3. y = x and y = 4. What is x?

    Answer

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

    Answer

  5. Same system. What is y?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y = 2x + 3 and y = 2x + 7. How many solutions?

    Answer

  2. y = 5x − 1 and 2y = 10x − 2. How many solutions?

    Answer

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

    Answer

Stretch Yourself

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

4 problems

  1. Match each graph situation with the number of solutions.

    Draw a line from each item on the left to its match on the right.

    • Lines cross once
    • Parallel lines
    • Identical lines
    • Exactly one solution
    • No solution
    • Infinitely many solutions

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

    Answer

  3. The Substitution

    y = 2x + 1 and 3x + y = 11. What is x?

    Answer

  4. The Other Half

    Same system. What is y?

    Answer