Linear Equations In Two Variables

Linear Equations In Two Variables When the equation is in the form ax + by + c = 0, where a , b , c are real numbers and a and b both are non zero then it is called Linear equation in two variables x and y. The Solution will include an ordered pair of real numbers which satisfy both the equations. 5x - 7y = 12 x 4y = 5 From the System of Linear Equations in Two variables x and y. Example 1: 5x - 7y = 12 equation 1 x 4y = 5 equation 2 This system of equation can be solved using Substitution method. Let us follow the example to understand better. Solution: From equation 2 we get x = 4 y + 5 Substitute x in Eq 1 5 * ( 4y+ 5 ) 7 y = 12 20y 7y = 12 25 So y = -1 Now we plug in y to get x x = 4y + 5 = 4 (-1) + 5 = 1 x = 1 ; y = -1 Example 2 4x 2 y = 6 equation 1 3x + 4y = 10 equation 2 This system of equation can be solved using Elimination method. Let us follow the example. Solution: In the first step we do equation 1 times 3 12x 6 y = 18 In the second step we do equation 2 times 4 12x + 16 y = 40 On subtracting we get - 22y = -22 y =1. We plug in y to find x so x = 2 x = 2 ; y = 1