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
1 · Read
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.
More to read
Graph points review (positive numbers only)
Pairs with a + b = 12 and both above 0 run from (1, 11) up to (11, 1). Listing them in order finds all eleven without missing any. Each pair adds back to 12, which checks it. Systematic listing beats guessing. The pair (12, 0) is out because zero is not allowed here.
Interpret relationships
Two part equations like 2x + y = 20 have many solutions. Pick x = 6 and y must be 8, since 12 + 8 = 20. Three working pairs are (3, 14), (6, 8) and (9, 2). Plugging each pair back in proves it.
Systems of equations with substitution
Generating solutions within a range needs a method. Fix one letter, solve for the other, then move on. For x + y = 15 with x twice y, only (10, 5) fits both clues. Testing every candidate keeps strays out.
Explore more
2 · Watch
به انگلیسیTake it off screen
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.
17 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.