8.
The value of x and y in equations 217x + 131y = 913 and 131x + 217y + 827 is
a) 2, 3
b) 4.2
c) 3,2
d) 5,4
Answers
Answer:
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Option -C
Step-by-step explanation:
Correction :-
131X+217Y = 827
Given :-
217X+131Y = 913
131X+217Y = 827
To find :-
Find the values of X and Y ?
Solution:-
Given equations are :-
217X+131Y = 913 ------------(1)
131X+217Y = 827 ------------(2)
On adding (1)&(2) then
217X+131Y = 913
131X+217Y = 827
(+)
________________
348X + 348Y = 1740
________________
=> 348X + 348Y = 1740
=> 348(X+Y) = 1740
=> X+Y = 1740/348
=> X+Y = 5 -----------------(3)
On Subtracting (2) from (1)
217X+131Y = 913
131X+217Y = 827
(-)
________________
86X -86Y = 86
________________
=> 86X -86Y = 86
=> 86(X-Y) = 86
=>X-Y = 86/86
=> X-Y = 1 ------------------(4)
On adding (3)&(4)
X+Y = 5
X-Y = 1
(+)
________
2X+0 = 6
________
=> 2X = 6
=> X = 6/2
=> X = 3
On Substituting the value of X in (3) then
=> 3+Y = 5
=> Y = 5-3
=> Y = 2
Therefore, X = 3 and Y = 2
Answer:-
The value of X = 3
The value of Y = 2
Check:-
If X = 3, Y = 2 then
LHS of (1)
=> 217(3)+131(2)
=> 641+262
=>913
=> RHS
LHS = RHS is true for X and Y
LHS of (2)
=> 131(3)+217(2)
=>393+434
=>827
=> RHS
LHS = RHS is true for X = 3 and Y = 2