Which statement about the solutions of $x - y = 0$ is correct?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

x - y = 0

means

x = y

, so (1, 1), (−4, −4) and (2.5, 2.5) all work — infinitely many points forming a line through the origin. A point like (3, 0) on the

x

-axis fails: 3 − 0 = 3 ≠ 0.

Answer: C) Every point whose two coordinates are equal is a solution

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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