How many solutions of $2 x + y = 10$ have BOTH $x$ and $y$ as positive whole numbers?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

x = 1

, 2, 3, 4 give

y = 8

, 6, 4, 2 — all positive.

x = 5

gives

y = 0

, which is not positive, and larger

x

makes

y

negative. So 4 pairs. (The equation itself still has infinitely many solutions once fractions and negatives are allowed.)

Answer: B) 4

Pick any value for one variable; solve for the other. Repeat to get many solutions.

Example:

3 x + 2 y = 12

.
- Let

x = 0 : 2 y = 12

→

y = 6

. So (0, 6) is a solution (this is the

y

-intercept).
- Let

x = 2 : 6 + 2 y = 12

→

y = 3

. So (2, 3) is a solution.
- Let

x = 4 : 12 + 2 y = 12

→

y = 0

. So (4, 0) is a solution (this is the

x

-intercept).
- Let

y = 0 : 3 x = 12

→

x = 4

. Same as above.

Four solutions found in seconds, and infinitely more available.

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