# LINEAR EQUATIONS IN TWO VARIABLE

## Linear equations in two variable of Class 9

### LINEAR EQUATIONS IN ONE VARIABLE

An equation of the form ax + b = 0 where a and b are real numbers and ‘x’ is a variable, is called a linear equation in one variable.

Here ‘a’ is called coefficient of x and ‘b’ is called as a constant term. i.e. 3x + 5 = 0, 7x – 2 = 0 etc.

## LINEAR EQUATIONS IN TWO VARIABLE

An equation of the form   ax + by + c = 0 or ax + by = c where a, b, c are real numbers,   a ≠ 0, b ≠ 0  and  x ,y are variables is called a linear equation in two variables.

Any pair of values of x and y which satisfies the equation a ≠ 0, b ≠ 0 is called a solution of it. ax + by + c = 0 In the equation ax + by + c = 0, if  a = 0 , b ≠ 0 or a ≠ 0 , b = 0 then the equation reduces to by = c or ax = c. i.e. we get equation in one variable. A linear equation in two variables has infinitely many solutions.

question . Prove that x = 3, y = 2 is a solution of 3x - 2y = 5.

Solution: x = 3, y = 2 is a solution of 3x - 2y = 5, because L.H.S. = 3x - 2y = 3 × 3 - 2 × 2 = 9 - 4 = 5 = R.H.S.

i.e. x = 3, y = 2 satisfied the equation 3x - 2y = 5. it is solution of the given equation.

question . Prove that x = 1, y = 1 as well as x = 2, y = 5 is a solution of 4x - y - 3 = 0.

Solution: Given eq. is 4x - y - 3 = 0 ....(i)

First we put x= 1, y = 1 in L.H.S. of eq...(i)

Here L.H.S. = 4x - y - 3 = 4 × 1 - 1 - 3 = 4 - 4 = 0 = R.H.S.

Now we put x = 2, y = 5 in eq. (i)

L.H.S. = 4x - y - 3 = 4 × 2 - 5 - 3 = 8 - 8 = 0 = R.H.S.

Since, x = 1, y = 1 and x = 2, y = 5 both pair satisfied in given equation therefore they are the solution of given equation.

question . Solve the equation and verify the answer.

Solution: …(i) ⇒ x = 48

Putting x = 48 in equation (i) we get

LHS, R.H.S.

Hence, L.H.S. = R.H.S