Cogito
Algebra 1 · Chapter 5 · Lesson 1
Substitution and Elimination
Two ways to remove a variable.
10 problems · about 20 minutes · A-REI.C.6
What this lesson teaches
The student solves systems of linear equations by substitution and by elimination.
- Both methods remove one variable.
- Substitution suits an equation solved for a variable.
- Elimination suits matching or easily matched coefficients.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
1 problemReview — Intercepts and Standard Form: 2x + 5y = 10. x-intercept?
Answer 5
Why 5.
Warm Up
Straightforward practice. Get the method working first.
4 problemsx + y = 15 and x − y = 3. What is x?
Answer 9
Why x = 9.
What do both methods achieve?
Answer They remove one variable.
Why Both eliminate a variable.
x + y = 12 and x − y = 2. What is x?
Answer 7
Why 2x = 14.
y = 2x and x + y = 9. What is x?
Answer 3
Why x + 2x = 9.
Build It Up
The same ideas with more to keep track of.
2 problems3x + y = 11 and y = x + 3. What is x?
Answer 2
Why 3x + x + 3 = 11.
2x + y = 7 and 2x − y = 1. What is y?
Answer 3
Why Subtract: 2y = 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsThe System: x + y = 10 and x − y = 4. What is x?
Answer 7
Why x = 7.
The Other Variable: x + y = 10 and x − y = 4. What is y?
Answer 3
Why y = 3.
The Tickets: Adult tickets cost 8 and child 5. 10 tickets cost 68. How many adult tickets?
Answer 6 adult tickets
Why 6 adult tickets.