One claim with two letters
A canteen sells puffs and chai. Two puffs and three chai cost ₹12. Is an equation like this linear in two letters? Try the cards.
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- Two puffs and three chai cost ₹12 in all.
- Call the puff price x and the chai price y.
2x + 3y = 12. The 2 and 3 are coefficients, the numbers in front of the letters.- Both letters carry power 1. No x times y.
The rule
Yes. The canteen bill is 2x + 3y = 12. It is linear in two letters.
Rule: A linear equation in two variables can be written ax + by + c = 0. Here a, b and c are fixed numbers. The numbers a and b are not both 0. Each letter has power 1, so there is no x² or y². x and y are never multiplied together.
Every term is a number times one letter, or a number alone. That is what "linear" means.
A coefficient is the number in front of a letter.
A letter may be missing. Then its coefficient is 0. 3x + 2 = 0 is 3x + 0y + 2 = 0.
x − y = 1 is linear in two variables too. Its coefficients are 1 and −1. A bare letter has a hidden coefficient of 1.
The standard form is ax + by + c = 0. For 2x + 3y = 12 move 12 to the left side: 2x + 3y − 12 = 0. So a = 2, b = 3 and c = −12.
One equation cannot give x and y separately. Many pairs fit it. Each equation here is a claim about x and y.
| Claim | Coefficient of x | Coefficient of y |
|---|---|---|
2x + 3y = 12 | 2 | 3 |
x − y = 1 | 1 | −1 |