Cogito
Grade 8 Math · Chapter 5 · Lesson 1
Where Two Lines Meet
A solution that satisfies both at once.
10 problems · about 19 minutes · 8.EE.C.8
What this lesson teaches
The child solves systems of two linear equations graphically and by substitution.
- A system needs one point that satisfies both equations.
- On a graph it is where the lines cross.
- Parallel lines give no solution.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — 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.
4 problemsy = 5x and y = 3x + 8. What is x?
Answer 4
Why x = 4.
What does it mean if two lines are parallel?
Answer The system has no solution.
Why Parallel lines never meet.
y = 2x and y = x + 5. What is x?
Answer 5
Why 2x = x + 5.
y = 5x and y = 2x + 9. What is x?
Answer 3
Why 3x = 9.
Build It Up
The same ideas with more to keep track of.
2 problemsy = 3x and y = 3x + 2. How many solutions?
Answer 0
Why Same slope, parallel.
y = 6x and y = 4x + 8. What is x?
Answer 4
Why 2x = 8.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Meeting Point: y = 4x and y = x + 6. What is x?
Answer 2
Why x = 2.
The Value of y: y = 4x and y = x + 6. What is y?
Answer 8
Why y = 8.