Class 10 Maths Linear Equations in 2 Variables | Pair Linear Equations in Two Variable |

**Pair Linear Equations in Two Variable**

Equation which can be put in form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. E.g. 3x + 10y =8

If it is given that sum of age of Students Ram & Sita is 9 & the difference in their age is 1, how can we find their age?

Here we can assume age of Ram to be x & that of Sita to be y & then create linear equations in 2 variable.

Sum of their age is 9, implies x+y=9

Difference of their age is 1, implies x-y=1

Now we can solve this pair of equation to find value of x & y, that is age of Ram & Sita.

These two linear equations are in the same two variables x and y. Equations like these are called a pair of linear equations in two variables.

The general form for a pair of linear equations in two variables x and y is

a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2} y + c_{2} = 0,

Where a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2} are all real numbers and a_{1}^{2} + b_{1}^{2} ≠ 0, a_{2}^{2} + b_{2}^{2} ≠ 0.

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