In the standard form ax + by + c = 0 of a linear equation in two variables, what condition must a and b satisfy?

Class 9Linear Equations in Two VariablesLinear Equations

ABoth a and b must be zero
BAt least one of a and b must be non-zero
CBoth a and b must be non-zero
Da and b must be equal

Step-by-Step Solution

By definition, a linear equation in two variables is ax + by + c = 0 where a, b, c are real numbers and at least one of a, b is non-zero (otherwise there is no variable).

Answer: B) At least one of a and b must be non-zero

Key idea: Graphing a linear equation

Three steps:

1. Find at least **two solutions** (preferably the

x

and

y

intercepts — easiest to plot).
2. Plot those points on the coordinate plane.
3. Draw a straight line through them.

Every linear equation in two variables graphs as a STRAIGHT LINE. (That's why they're called 'linear'.)

For accuracy: find a third solution and verify it lies on the line — catches arithmetic mistakes.

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