A linear equation in one variable, such as $2 x + 5 = 0$ , has how many solutions when treated as an equation in ONE variable?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

In one variable,

2 x + 5 = 0

gives

x = - \frac{5}{2}

, a single unique value. (Only equations in two variables have infinitely many solutions.)

Answer: A) One unique 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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