Equations with Two Unknowns
Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)
What a learner can do afterwards
- List all whole-number pairs (a, b) where a + b = 12 with a, b > 0
- Find three pairs that satisfy 2x + y = 20
- Explain systematically how to generate all integer solutions to a two-variable equation within a given range
The lesson
You know how to write an equation like a + b = 10. Now think about solving it. This equation does not have just one answer. It has many. Any pair of numbers that adds up to 10 makes the equation true.
Mia wants a pair of numbers for 2x + y = 20. She picks x = 5. Two times 5 is 10, so y must be 10 to make the total 20. The pair (5, 10) works.
To find more pairs, pick a number for one unknown, then work out what the other one has to be. Change your first pick and you get a new pair every time.
Many pairs of numbers can make the same equation true. Pick one unknown, solve for the other, and you have found a pair.
Watch it
Where it sits
Learn first
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.