MAMMAIR OR
LINFARTOUATIONS
IN
TWO
VARIABLES
ther with the charge for
paid is 105 and for
travelling a distance
ecomes
and the denominat
0
Is son. Five you
present ages?
So, the solution of the equations in a = 2000, y = 4000. Therefore, the monthly income
he fixed charges and for the persons are p 1,000 and e 14,000, respectively,
Verification : 18000.: 14000 = 9: 7. Also, the ratio of their expenditures
18000 - 2000: 14000 - 2000 = 16000: 12000 =4:3
ariable. The
this method
of the
1. The method used in solving the example above is called the elimination method,
because we eliminate one variable first, to get a linear equation in one variable,
In the example above, we eliminated y, We could also have eliminated x, Try
doing it that way
2. You could also have used the substitution, or graphical method, to solve this
problem. Try doing so, and see which method is more convenient,
Let us now note down these steps in the elimination method:
Step 1: First multiply both the equations by some suitable non-zero constants to make
the coefficients of one variable (ether or y) numerically equal,
and the Step 2 Then add or subtract one equation from the other so that one variable gets
eliminated. If you get an equation in one variable, go to Step 3.
If in Step 2, we obtain a true statement involving no variable, then the original
pair of equations has infinitely many solutions,
ation
If in Step 2, we obtain a false statement involving no variable, then the original
pair of equations has no solution, Le, it is inconsistent,
Step 3: Solve the equation in one variable (x or y) so obtained to get its value,
Step 4: Substitute this value of x (or y) in olther of the original equations to get the
value of the other variable,
Now to Hlustrate it, we shall solve few more examples,
example 12 : Use elimination method to find all possible solutions of the following
air of linear equations
2x + 3y = 8
(1)
4x + 6y - 7
(2)
ion:
3
Multiply Equation (1) by 2 and Equation (2) by 1 to make
onts of x equal. Then we get the equations as:
4x + 6y - 16
4x + 6y
LINFARTOUATIONS
IN
TWO
VARIABLES
ther with the charge for
paid is 105 and for
travelling a distance
ecomes
and the denominat
0
Is son. Five you
present ages?
So, the solution of the equations in a = 2000, y = 4000. Therefore, the monthly income
he fixed charges and for the persons are p 1,000 and e 14,000, respectively,
Verification : 18000.: 14000 = 9: 7. Also, the ratio of their expenditures
18000 - 2000: 14000 - 2000 = 16000: 12000 =4:3
ariable. The
this method
of the
1. The method used in solving the example above is called the elimination method,
because we eliminate one variable first, to get a linear equation in one variable,
In the example above, we eliminated y, We could also have eliminated x, Try
doing it that way
2. You could also have used the substitution, or graphical method, to solve this
problem. Try doing so, and see which method is more convenient,
Let us now note down these steps in the elimination method:
Step 1: First multiply both the equations by some suitable non-zero constants to make
the coefficients of one variable (ether or y) numerically equal,
and the Step 2 Then add or subtract one equation from the other so that one variable gets
eliminated. If you get an equation in one variable, go to Step 3.
If in Step 2, we obtain a true statement involving no variable, then the original
pair of equations has infinitely many solutions,
ation
If in Step 2, we obtain a false statement involving no variable, then the original
pair of equations has no solution, Le, it is inconsistent,
Step 3: Solve the equation in one variable (x or y) so obtained to get its value,
Step 4: Substitute this value of x (or y) in olther of the original equations to get the
value of the other variable,
Now to Hlustrate it, we shall solve few more examples,
example 12 : Use elimination method to find all possible solutions of the following
air of linear equations
2x + 3y = 8
(1)
4x + 6y - 7
(2)
ion:
3
Multiply Equation (1) by 2 and Equation (2) by 1 to make
onts of x equal. Then we get the equations as:
4x + 6y - 16
4x + 6y
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