|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
a1x + b1y + c1 = 0 and a2x + b2 y + c2 = 0,
Where a1, b1, c1, a2, b2, c2 are all real numbers and a12 + b12 ≠ 0, a22 + b22 ≠ 0.