In Substitution method, find the value of any one variable ( x or y) from one equation and put it in other equation and then solve it like a simple equation.
Solve the following using Substitution -method
1) Find the solution by Substitution -method 2x + y = 6 and 2x – y = -2 Solution: 2x + y = 6 ------>(1) and 2x – y = -2 -------> (2) y = -2x + 6 Put y = -2x + 6 in equation (2) 2x – ( -2x + 6 ) = -2 2x + 2x – 6 = -2 ( use a distributive law) 4x – 6 = - 2 4x = -2 + 6 4x = 4
x = 1
Now put x =1 in any one of the given equation. Equation (1) ⇒ 2 (1) + y = 6 2 + y = 6 y = 6 – 2 y = 4 Solution is
(1,4)
_________________________________________________________________ Example 2 : 3x + 2y + 25 = 0 and 2x + y + 10 = 0 Solution : 3x + 2y = -25 -----> (1) and 2x + y = -10 -----> (2) y = -2x – 10 Put y = -2x – 10 in equation (1) 3x + 2( -2x -10) = -25 3x – 4x – 20 = -25 ( use a distributive law) - x – 20 = -25 -x = -25 + 20 -x = -5
x = 5
Now put x = 5 in equation (1) Equation (1) ⇒ 3(5) + 2y = -25 15 + 2y = -25 2y = -25 -15 2y = - 40 y = - 20 Solution is