Substitution Method

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)

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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

(5,-20)

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Linear equation in two variables

• Solving linear equation by graphical method.
• Substitution method.
• Solving system of equation by elimination method
• Cross multiplication method or Cramer’s rule

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