Cogito
Integrated Math 1 · Chapter 3 · Lesson 2
Solving Systems by Elimination
Add the equations and lose a variable.
12 problems · about 21 minutes · A-REI.C.5, A-REI.C.6
What this lesson teaches
The student solves systems by elimination, scaling equations where needed.
- Adding two equations eliminates a variable when its coefficients are opposites.
- Scale one or both equations to create those opposites.
- Substitution suits a coefficient of 1; elimination suits standard form.
Warm Up
Straightforward practice. Get the method working first.
5 problemsx + y = 12 and x − y = 2. What is x?
Answer 7
Why 7.
Why may an equation be multiplied by a constant?
Answer Scaling both sides equally leaves the same solutions.
Why The solution set is unchanged.
x + y = 10 and x − y = 4. What is x?
Answer 7
Why Add to get 2x = 14.
Same system. What is y?
Answer 3
Why 10 − 7.
3x + y = 10 and 2x − y = 5. What is x?
Answer 3
Why Add to get 5x = 15.
Build It Up
The same ideas with more to keep track of.
3 problems2x + 2y = 14 and x − y = 1. What is x?
Answer 4
Why Halve the first, then add.
To eliminate from 2x and 3x, what common multiple do you scale to?
Answer 6
Why The lowest common multiple.
Does multiplying an equation throughout change its solutions? 1 yes, 0 no.
Answer 0
Why Both sides scale equally.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each system by the better first method.
Answer Substitution: y = 3x + 2 and 2x + y = 12, x = 5 − y and 3x + y = 11 · Elimination: 2x + 3y = 12 and 4x − 3y = 6, 5x + 2y = 9 and 3x − 2y = 7
Why An equation already solved for a variable invites substitution.
4x + y = 14 and 2x − y = 4. What is x?
Answer 3
Why Add to get 6x = 18.
The Cancellation: 2x + 3y = 12 and 4x − 3y = 6. What is x?
Answer 3
Why 3.
The Second Value: Same system. What is y?
Answer 2
Why 2.