if
a+e=0
b+f=0
4a+c+2e=0
4b+d+2f=0
3a+3c+e=3
3a+3d+f=1
then find out a,b,c,d,e,f
values
Answers
Step-by-step explanation:
Given:-
a+e=0
b+f=0
4a+c+2e=0
4b+d+2f=0
3a+3c+e=3
3a+3d+f=1
To find :-
Find the values of a,b,c,d,e,f ?
Solution :-
Given equations are:
a+e=0 ---------(1)
=> a = -e -------(2)
b+f=0----------(3)
=> b = -f -------(4)
4a+c+2e=0-----(5)
On Substituting the value of a in (5)
=>4(-e)+c+2e = 0
=> -4e+c+2e = 0
=> c-2e = 0
=> c = 2e--------(6)
4b+d+2f=0-----(7)
3a+3c+e=3-----(8)
On substituting the values of a and e from (2) and (6)
=> 3(-e) + 3(2e)+ e = 3
=> -3e+6e+e = 3
=> 7e-3e = 3
=> 4e = 3
=> e = 3/4--------(8)
If e = 3/4 then a = -e = -3/4
a = -3/4
and if e = 3/4 then c = 2e
=> c = 2(3/4)
=> c = 6/4
=> c = 3/2
and
from (7) 4b+d+2f=0
=> 4(-f)+d+2f = 0
=> -4f+d+2f = 0
=> d-2f = 0
=> d = 2f-------(8)
3a+3d+f=1 -----(9)
Now
on Substituting the values of a ,d in (9)
3(-3/4)+3(2f)+f = 1
=> (-9/4)+6f+f = 1
=> (-9/4)+7f = 1
=> 7f = 1+(9/4)
=> 7f = (4+9)/4
=> 7f = 13/4
=> f = 13/(4×7)
=>f = 13/28
if f = 13/28
=> d = 2f
=> d = 2(13/28)
=>d = 26/28
=> d = 13/14
we have b = -f
=>b = -13/28
Answer :-
The value of a = -3/4
The value of b = -13/28
The value of c = 3/2
The value of d =13/14
The value of e = 3/4
The value of f = 13/28
Used method :-
Method of Substitution
Check:-
I)a+e = 0
=> (-3/4)+(3/4)
=>>(-3+3)/4
=> 0/4
=>>0
ii)b+f=0
(-13/28)+(13/28)
=>>(-13+13)/28
=> 0/28
=>0
iii)4a+c+2e=0
=> 4(-3/4)+(3/2)+2(3/4)
=> -3+(3/2/+(3/2)
=>(-6+3+3)/2
=>>(-6+6)/2
=> 0/2
=> 0
iv)4b+d+2f=0
=> 4(-13/28)+(13/14)+2(13/28)
=>>(-52/28)+(13/14)+(13/14)
=>>(-52+26+26)/28
=>>(-52+52)/28
=>>0/28
=>0
v)3a+3c+e=3
3(-3/4)+3(3/2)+(3/4)
=> (-9/4)+(9/2)+(3/4)
=>>(-9+18+3)/4
=>>(21-9)/4
=>12/4
=> 3
vi)3a+3d+f=1
=> 3(-3/4)+3(13/14)+(13/28)
=> (-9/4)+(39/14)+(13/28)
=>(-63+78+13)/28
=> 28/28
=> 1
Verified all the relations in the problem are true for the values
Answer:
ANSWER IN THE ATTACHMENT.
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