Solve any word sum based on Linear equations in two variables by all the three methods
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TO DETERMINE
Solve any word sum based on Linear equations in two variables by all the three methods
CONCEPT TO BE IMPLEMENTED
There are three methods to solve systems of linear equations in two variables:
1. Graphical method
2. Substitution method
3. Elimination method
EVALUATION
We first consider the problem as below :
Sum of two numbers is 9 and their difference is 3 . Find the numbers
Formation of system of equations :
Let the numbers are x and y where x > y
Now it is given that sum is 9
Thus we get x + y = 9
Again it is given that their difference is 3
Thus we get x - y = 3
So the given system of equations are
x + y = 9 - - - - - - (1)
x - y = 3 - - - - - - - (2)
SOLVE BY GRAPHICAL METHOD
The given system of equations are
x + y = 9 - - - - - - (1)
x - y = 3 - - - - - - - (2)
Graph : Graph is referred to the attachment
In the graph we plot the lines
The two lines intersect at (6,3)
So we get x = 6 & y = 3
So first number = 6 and second number = 3
SUBSTITUTION METHOD
The given system of equations are
x + y = 9 - - - - - - (1)
x - y = 3 - - - - - - - (2)
From Equation 1 we get y = 9 - x
Putting the value of y in Equation 2 we get
x - ( 9 - x ) = 3
⇒ x - 9 + x = 3
⇒ 2x - 9 = 3
⇒ 2x = 12
⇒ x = 6
From Equation 1 we get
y = 9 - 6 = 3
So first number = 6 and second number = 3
ELIMINATION METHOD
The given system of equations are
x + y = 9 - - - - - - (1)
x - y = 3 - - - - - - - (2)
Adding Equation 1 and Equation 2 we get
⇒ 2x = 12
⇒ x = 6
From Equation 1 we get
y = 9 - 6 = 3
So first number = 6 and second number = 3
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