Cogito
Grade 8 Math · Chapter 5 · Lesson 3
Solving a System by Elimination
Add the equations and one letter disappears.
10 problems · about 20 minutes · 8.EE.C.8
What this lesson teaches
The child solves a system by adding or subtracting the two equations.
- Elimination adds or subtracts the equations to remove one letter.
- Opposite signs are added; matching signs are subtracted.
- Scale one equation first when no pair of coefficients matches.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Solving a System by Substitution: y = 4x and x + y = 15. What is x?
Answer 3
Why x = 3.
Review — Where Two Lines Meet: y = 5x and y = 3x + 8. What is x?
Answer 4
Why x = 4.
Review — Writing Equations from Situations: 6 + 5m = 3m + 20. What is m?
Answer 7
Why m = 7.
Warm Up
Straightforward practice. Get the method working first.
3 problemsx + y = 12 and x − y = 4. What is x?
Answer 8
Why x = 8.
x + y = 9 and x − y = 3. What is x?
Answer 6
Why 2x = 12.
Same system. What is y?
Answer 3
Why 6 + y = 9.
Build It Up
The same ideas with more to keep track of.
2 problems2x + y = 11 and x + y = 7. What is x?
Answer 4
Why Subtract the second from the first.
Same system. What is y?
Answer 3
Why 4 + y = 7.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Sum: x + y = 10 and x − y = 2. What is x?
Answer 6
Why x = 6.
The Other: Same system. What is y?
Answer 4
Why y = 4.