Sonu says (4, 4) is a solution of $x + 4 y = 20$ ; Ravi says (16, 1) is. Who is right?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

Sonu: 4 + 4(4) = 20 ✓. Ravi: 16 + 4(1) = 20 ✓. Both pairs satisfy the equation, and that is normal — every point of the line is a solution.

Answer: A) Both are right — one equation in two variables has infinitely many solutions

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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