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Home >> Linear Equations >> Linear Equation in Two Variables >>

Linear Equation in Two Variables

Linear Equations Complex Examples Linear Equation in one Variable Linear Equation in Two Variables Difference between Linear Equation in One & Two Variables Linear Expression

Before you understand Linear Equation in Two Variables, you are advised to read:

What is Linear Equations in One Variable ?

What is Linear Equations in Two Variables

Linear Equations which are written in the form of; ax + by + c = 0,
Where a, b, c are real numbers and a, b, c are both not equal to Zero. Such Linear Equations are known as Linear Equations in Two Variables.

Example: In a cricket match, batsman 1 & batsman 2 together scored 100 runs. Express this in the form of linear equation:
Solution: As per the question:
Let Batsman 1 = a
Batsman 2 = b

Since both batsmen together scored 100 runs, so we get:
a + b = 100

or we can also write it as:
a + b 100 = 0

And you can see that the above equation is in the form of ax + by + c = 0, Hence, this forms a linear equation in two variables.

Solving Linear Equations in Two Variables

As we know that Linear Equations with two variables are written in the form of; ax + by + c = 0, So, we get the solution when we find the values of both variables i.e. x and y.

Unlike, Linear Equation in One variable which has a unique solution; linear equation in two variable has infinitely many solution.

Example: x + y = 15
In the given linear equation with two variable x and y, we can have following multiple solutions:

Solution 1: If x = 0, then we get:
0 + y = 15
Or
y = 15
So, x = 0 & y = 15 and solution of linear equation is (0 , 15)

Solution 2: If x = 2, then we get:
2 + y = 15
Subtract 2 from both sides and we get:
y = 13
So, x = 2 & y = 13 and solution of linear equation is (2 , 13)

Solution 3: If y = 3, then we get:
x + 3 = 15
Subtract 3 from both sides and we get:
x = 12
So, x = 12 & y = 3 and solution of linear equation is (12 , 3)

Solution 4: If y = 5, then we get:
x + 5 = 15
Subtract 5 from both sides and we get:
x = 10
So, x = 10 & y = 5 and solution of linear equation is (10 , 5)

From the above solution 1, 2, 3 & 4 you can observe that linear equation in two variables has infinitely many solutions.
Also, note that while writing the solution, first write the value of x and then the value of y.


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