Cogito
Integrated Math 1 · Chapter 3 · Lesson 1
Solving Systems by Graphing and Substitution
Where two conditions meet.
12 problems · about 21 minutes · A-REI.C.6
What this lesson teaches
The student solves systems of linear equations by graphing and by substitution.
- A solution satisfies every equation in the system at once.
- Substitution replaces one variable with an equivalent expression.
- Lines can meet once, never, or everywhere.
Warm Up
Straightforward practice. Get the method working first.
5 problemsy = 2x and y = x + 5. What is x?
Answer 5
Why 5.
What does a solution to a system mean graphically?
Answer The point where the lines cross.
Why The intersection point.
y = x and y = 4. What is x?
Answer 4
Why They are equal.
y = 3x and y = x + 4. What is x?
Answer 2
Why 3x = x + 4.
Same system. What is y?
Answer 6
Why 3 × 2.
Build It Up
The same ideas with more to keep track of.
3 problemsy = 2x + 3 and y = 2x + 7. How many solutions?
Answer 0
Why Same slope, different intercept.
y = 5x − 1 and 2y = 10x − 2. How many solutions?
Answer 0
Why Enter 0 for infinitely many, since the lines coincide.
x + y = 10 and x − y = 2. What is x?
Answer 6
Why Add the equations.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each graph situation with the number of solutions.
Answer Lines cross once → Exactly one solution; Parallel lines → No solution; Identical lines → Infinitely many solutions
Why Parallel lines never meet.
y = 4x and y = 2x + 6. What is x?
Answer 3
Why 2x = 6.
The Substitution: y = 2x + 1 and 3x + y = 11. What is x?
Answer 2
Why 2.
The Other Half: Same system. What is y?
Answer 5
Why 5.