If 49 x – 57 y = 172 and 57 x – 49 y = 252 then x + y =?
Answers
Step-by-step explanation:
Given:-
49 x – 57 y = 172 and 57 x – 49 y = 252
To find:-
Find the value of x+y ?
Solution:-
Given pair of linear equations are
49 x – 57 y = 172 -----------(1)
57 x – 49 y = 252-----------(2)
On subtracting (1) from (2)
57 x – 49 y = 252
49 x – 57 y = 172
(-)
______________
8 x + 8 y = 80
_______________
=>8 x + 8 y = 80
=>8 ( x + y ) = 80
=> x + y = 80/8
=> x + y = 10
Answer:-
The value of x + y for the given problem is 10.
Check:-
On adding equations (1)&(2) then
49 x – 57 y = 172
57 x – 49 y = 252
(+)
_______________
106 x - 106 y = 424
_______________
=>106 x - 106 y = 424
=>106 ( x - y) = 424
=>x - y = 424/106
=> x - y = 4 -----------------(3)
and x + y = 10 -------------(4)
On adding them
2x + 0 = 14
=>2x = 14
=>x = 14/2
=>x = 7
from (4)
7+y = 10
=>y = 10-7
=>y = 3
The value of x = 7 and y = 3
x+y = 7+3 = 10
49(7)-57(3)
=>343-171
=>172
and
57(7)-49(3)
=>399-147
=>252
Verified the given relations