Mathematics: Solving Simultaneous Equations using Substitution Method

1. Linear Equations in Two
Variables
Solving Simultaneous Equations using Substitution Method
BY
SHRUTI DASGUPTA
10. 12.2020 CLASS 9th

2. Let’s Recall
Ques1. Can you give me an example of Linear Equation?
• x + y = 1; 3x – y = 5, ……..
Ques2. What are Simultaneous Equations?
• When we consider two Linear Equations at the same time in the
same two variables are called Simultaneous Equations.
Ques3. Can you tell me a method to solve Simultaneous
Equation?
• Elimination Method

3. General Form of Linear Equation in
Two Variables
The general form is given as:
ax + by + c = 0
where;
• a, b, c, are real non-zero numbers
• x, y are variables
• the index of x and y is 1.
• since the index is 1, they are called as Linear Equations

4. Example
• Solve for value of x and y
• 3x + y = 5 …………….(1)
• 2x + 3y = 1 …………..(2)
• SOLUTION:
In the given equation (1) and
(2), make any one co-efficient
equal.
Multiplying (1) by 3 and (2)
by 1, we get:
(3x + y ) X 3 = 5 X 3
⟹ 9x + 3y = 15 ………..(3)
2x + 3y = 1 …………..(2)
Subtract (2) from (3)
9x + 3y = 15
- ( 2x + 3y = 1 )
⟹ 7x + 0 = 14
⟹ x = 14 /7 ⟹ x = 2
Put value of x in (1)
Then, 3x + y = 5 becomes:
⟹ 3X2 + y = 5
⟹ 6 + y = 5
⟹ y = -1
Thus, values of x and y are :
x = 2 y = -1

5. Substitution Method
• In this method we express one variable in terms of the other
variable to arrive at a solution.
• EXAMPLE:
In the previous example we have:
• 3x + y = 5 …………….(1)
• 2x + 3y = 1 …………..(2)
• Here we can write (1) as:
• y = 5 – 3x
• And put this value of y in (2) to get solution for value of x and y.

6. Example 1:
• Solve for value of x and y
• 8x + 3y = 11 ………. (1)
• 3x – y = 2 …………… (2)
• SOLUTION:
From (2) we can see that:
3x – y = 2 ⟹ 3x – 2 = y
Substituting this value of y in
(1) we get:
8x + 3y = 11
⟹ 8x + 3 ( 3x – 2) = 11
⟹ 8x + 9x – 6 = 11
⟹ 17x = 11 + 6
⟹ 17x = 17
⟹ x = 1
Put value of x in 3x – 2 = y, we
get:
⟹ 3x – 2 = y
⟹ 3X1 – 2 = y
⟹ 3 – 2 = y
⟹ y = 1
Thus, values of x and y are :
x = 1 y = 1

7. Example 2:
• Solve for value of x and y
• 3x – 4y = 16 ………….. (1)
• 2x – 3y = 10 …………… (2)
• SOLUTION:
From (1) we can see that:
⟹ 3x – 4y =16
⟹ 3x = 16 + 4y
⟹ x =
(16 + 4y)
3
Substituting the value of x in (2) we
get:
2x – 3y = 10
⟹ 2 {
(16 + 4y)
3
} – 3y = 10
⟹{
32 + 8y
3
} – 3y =10
⟹
32 + 8y – 9y
3
= 10
⟹ 32 – y = 30
⟹ 32 – 30 = y
⟹ y = 2
Put value y in x =
(16 + 4y)
3
we get:
⟹ x =
(16 + 4 X 2)
3
⟹ x =
(16 + 8)
3
⟹ x =
24
3
⟹ x = 8
Thus, values of x and y are :
x = 8 y = 2

8. Recapitualtion
Ques 1. What is the general form of Linear Equation?
Ques 2. What is the index of Linear Equation?
Ques 3. How do we solve Linear Equation with Substitution
Method?

9. Application-based Question
Ques. Write 3 solutions for the equation:
x + y = 7

10. Homework
Ques. Solve for the values of x and y:
a) x + y = 4
2x – 5y = 1
b) 3x – 5y = 16
x – 3y = 8

11. THANK YOU