Cogito
Grade 8 Math · Chapter 5 · Lesson 2
Solving a System by Substitution
Replace one letter and one equation is left.
10 problems · about 20 minutes · 8.EE.C.8
What this lesson teaches
The child solves a system of two linear equations by substitution.
- Substitution replaces one letter with an expression in the other.
- That leaves one equation in one unknown, which can be solved.
- Put the answer back to find the second value, then check both equations.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — 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.
Review — Equations with Brackets and Fractions: 5(x + 1) = 40. What is x?
Answer 7
Why x = 7.
Warm Up
Straightforward practice. Get the method working first.
3 problemsy = 4x and x + y = 15. What is x?
Answer 3
Why x = 3.
y = x + 2 and x + y = 10. What is x?
Answer 4
Why x + x + 2 = 10.
Same system. What is y?
Answer 6
Why y = x + 2.
Build It Up
The same ideas with more to keep track of.
2 problemsy = 2x and 3x + y = 20. What is x?
Answer 4
Why 3x + 2x = 20.
Does a solution have to satisfy both equations? 1 for yes, 0 for no.
Answer 1
Why That is what a system means.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Substitution: y = 3x and x + y = 12. What is x?
Answer 3
Why x = 3.
The Other Half: Same system. What is y?
Answer 9
Why y = 9.