## 1. Linear equations in two variables.

Equation ax + by + c = 0 is a linear equation in two variable x and y.

where a , b , c are real numbers ( a ≠ 0 and b ≠ 0 )

## 2. Solution of linear equations in two variables.

If x = α and y = β is solution of ax + by + c = 0 then aα + bβ + c = 0

## Note Points of Linear Equations in Two Variables.

(i). The equation ax + by + c = 0 has infinitely many solution.

(ii). The graph of the equation ax + by + c = 0 is a straight line.

(iii). The equation of x – axis is y = 0.

(iv). The equation of y – axis is x = 0.

(v). The equation of straight line which ll to x – axis is y = b.

(vi). The equation of straight line which ll to y – axis is x = a.

(vii). The equation of straight line which ⊥ on x – axis is x = a.

(viii). The equation of straight line which ⊥ on y – axis is y = b.

## 3. Graph of linear equations.

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