Question

how many solutions can linear equation in two veriable have?

Answer 1

it can have infinite solutions.

Answer 2

Linear equation in two variables have solution according to some Condition .

Let us assume two linear equation as

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

• For Unique Solution

a1 / a2 ≠ b1 /b2

And this line cut at a point giving a unique solution also known as consistent.

• For infinity Solution

a1 / a2 = b1 / b2 = c1 /c2

And this line is coincide having infinity number of solution it is also known as consistent.

• For No Solution

a1 / a2 = b1 / b2 ≠ c1 / c2

And this line is parallel to each other having no solution also known as inconsistent.