3 Solve the following pair of linear equations by
elimination method.
(i) 89x + 91 y = 449, 91x + 89 y = 451
(ii) 117x +231 y = 579, 231x + 117 y = 465
(iii) 217x+131y =913, 131x+217 y = 827
(iv) 41 x - 17 y = 99,17 x -- 41 y = 75
(v) 23x-29 y = 98,29x -23y = 110
nobody can solve all question
Answers
(I) 89x+91y=449
91x+89y=451
, x-y=1......... (1)
By adding we get
89x+91y=449
91x+89y=451.
, X+y=5..........(2)
add eqn (1) and (2)
, X=3 and y=2
(II) for 1st equation :-
117x+231y=579. -(1)
for 2nd equation:-
231x+117y=465. -(2)
Adding both equations (1) and (2):-
equation 1:-117x+231y=579
equation 2:-231x+117y=465
=>348x+348y=1044
=>x+y=1044/348=3
=>x+y=3 -(3)
equation 3:- x+y=3
Subtraction both equations (1) and (2):-
equation 1:-117x+231y=579
equation 2:--231x-117y=-465
=>-114x+114y=114
=>-x+y=144/144=1
=>-x+y=1 -(4)
equation 4:- -x+y=1
On Solving equation 3 and 4 we get :-
x=1 & y=2
(III)217x + 131y= 913 .......( 1 )
131x +217y = 827........( 2 )
Adding equation ( 1 ) and equation ( 2 ),we get
( 217x + 131y ) + ( 131x + 217y) = 913 + 827
⇒ 348x + 348y = 1740
⇒ x + y = 5 ........( 3 )
Subtracting equation ( 2 ) from equation ( 1 ), we get
86x - 86y = 86
⇒ x - y = 1 ...........( 4 )
Adding equations ( 3 ) and ( 4 ) , we get
☆ 2x = 6 ⇒ x = 3
Subtracting equation ( 4 ) from ( 3 ), we get
☆ 2y = 4 ⇒ y = 2
Hence, the solution is x = 3 and y = 2 .
(IV) 41x - 17y = 99
17x - 41y = 75
24x + 24y = 24
Therefore x + y =1
41x - 17y = 99
17x - 41y = 75
58x - 58y = 174
Therefore x - y = 3
Now simplifying the 2 equations x + y =1 and x - y = 3 we get
Y = -1; x = 2
(V) 23x - 29y = 98 ------1)
29x - 23y = 110 --------2)
Adding 1st both equation ..
23x - 29y = 98
29x - 23y = 110
_____________
52x - 52y = 208
x - y = 4 --------3 )
After that substracting equation 1st from 2nd
29 x- 23y = 110
23x - 29 y = 98
6x+ 6y = 12
x + y = 2 -------------4)
solving 3 and 4 tha equation ..
x = 3 and y = - 1
PLS MARK BRAINLIEST