Linear Equation in Two Variables

Linear Equation in one Variable	Linear Equation in Two Variables	Difference between Linear Equation in One & Two Variables	Linear Expression	Linear Equations Complex Examples
Solving a Pair of Linear Equations

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.