SOLVING SYSTEM OF LINEAR EQUATIONS IN THREE VARIABLES
Solving System of Linear Equations in Three Variables :
Here we are going to see, how to solve system of linear equations in three variables.
Procedure for solving system of linear equations in three variables :
Step 1 :
By taking any two equations from the given three, first multiply by some suitable non-zero constant to make the co-efficient of one variable (either x or y or z) numerically equal.
Step 2 :
Eliminate one of the variables whose co-efficients are numerically equal from the equations.
Step 3 :
Eliminate the same variable from another pair.
Step 4 :
Now we have two equations in two variables.
Step 5 :
Solve them using any method studied in earlier classes
Step 6 :
The remaining variable is then found by substituting in any one of the given equations.
Solving Systems of Linear Equations in Three Variables Example Problems
Question 1 :
Solve the following system of linear equations in three variables
(i) x + y + z = 5 ; 2x − y + z = 9 ; x − 2y + 3z = 16
Solution :
x + y + z = 5 -------(1)
2x − y + z = 9 -------(2)
x − 2y + 3z = 16 -------(3)
|
Let us add (1) and (2)  |
Multiply the first equation by 2 and add by (3)  |
Let 3x + 2z = 14 ----(4) and 3x + 5z = 26 ---(5)
(4) - (5)
3x + 2z = 14
3x + 5z = 26
(-) (-) (-)
----------------
-3z = -12 ==> z = 4
By applying z = 4 in (4), we get
3x + 2(4) = 14
3x + 8 = 12
3x = 14 - 8
3x = 6 ==> x = 2
By applying x 2 and z = 4 in (1), we get
2 + y + 4 = 5
6 + y = 5
y = 5 - 6
y = -1
Hence the required solution is x = 2, y = -1 and z = 2.
After having gone through the stuff given above, we hope that the students would have understood, "Solving System of Linear Equations in Three Variables".
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