Solve these linear equation in three variable.
Answers
Step-by-step explanation:
Given :-
0 = a+b+c
1 = -2a-2c
0 = -a-3b+2c
To find:-
Solve these linear equation in three variables?
Solution :-
Given equations are :
0 = a+b+c --------------(1)
1 = -2a-2c --------------(2)
0 = -a-3b+2c ----------(3)
On taking (1)
=> a+b+c = 0
=> a+c = -b -------------(4)
On taking (2)
1 = -2a-2c
=> -2a-2c = 1
=> 2a+2c = -1----------(5)
=> 2(a+c) = -1
=> a+c = -1/2-------------(6)
From (4)&(6)
-b = -1/2
=> b = 1/2
on taking (3)
0 = -a-3b+2c
=> -a-3(1/2)+2c = 0
=> -a-(3/2)+2c = 0
=> (-2a-3+4c)/2 = 0
=>-2a-3+4c = 0×2
=> -2a+4c -3 = 0
=> -2a+4c = 3
=> 2a-4c = -3 -----------(7)
On Subtracting (5) from (7)
2a-4c = -3
2a+2c = -1
(-)
_________
0-6c = -2
_________
=> -6c = -2
=> 6c = 2
=>c = 2/6
=>c = 1/3
On Substituting the value of c in (6)
=> a+(1/3) = -1/2
=> a = (-1/2)-(1/3)
LCM of 2 and 3 = 6
=> a = (-3-2)/6
=> a = -5/6
Therefore, a = -5/6 , b = 1/2 , c = 1/3
Answer:-
The value of a = -5/6
The value of b = 1/2
The value of c = 1/3
Solution for the given linear equations in three variables is ( -5/6 , 1/2 , 1/3 )
Check:-
a = -5/6 , b = 1/2 , c = 1/3
a+b+c
=> (-5/6)+(1/2)+(1/3)
=> (-5+3+2)/6
=> (5-5)/6
=>0/6
=>0
a+b+c = 0
and
-2a-2c
=> -2(-5/6)-2(1/3)
=> (5/3)-(2/3)
=> (5-2)/3
=> 3/3
=> 1
-2a-2c = 1
and
-a-3b+2c
=>-(-5/6)-3(1/2)+2(1/3)
=> (5/6)-(3/2)+(2/3)
=>(5-9+4)/6
=> (9-9)/6
=> 0/6
=> 0
-a-3b+2c = 0
Verified the given relations in the given problem.