Cogito
Algebra 1 · Chapter 5 · Lesson 3
Systems in Context
Two unknowns, two conditions.
11 problems · about 23 minutes · A-CED.A.3
What this lesson teaches
The student writes and solves a system modelling a real situation.
- Two unknowns need two independent conditions.
- Each condition in the story becomes one equation.
- Finish by answering in the words of the problem, not as bare numbers.
Warm Up
Straightforward practice. Get the method working first.
4 problemsx + y = 12 and x − y = 2. What is x?
Answer 7
Why 7.
x + y = 10 and x − y = 4. What is x?
Answer 7
Why Add the equations.
Same system. What is y?
Answer 3
Why 7 + y = 10.
How many equations are needed for two unknowns?
Answer 2
Why One per unknown.
Build It Up
The same ideas with more to keep track of.
3 problems2x + y = 12 and y = 4. What is x?
Answer 4
Why 2x = 8.
20 coins are 5p and 10p, worth 150p. If there are 10 tens, how many fives?
Answer 10
Why 20 − 10.
Order the steps for a system word problem.
Answer 1. Name both unknowns 2. Write one equation per condition 3. Solve the system 4. Answer in the words of the problem
Why Naming comes before writing.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsx + y = 9 and x = 2y. What is y?
Answer 3
Why 3y = 9.
Same system. What is x?
Answer 6
Why Twice y.
The Count: a + c = 15 and a = 7. What is c?
Answer 8
Why 8.
The Money: 7 adults at £8 each. How much, in pounds?
Answer 56
Why £56.