Question

solve for x and y:99x + 101y=499 and 101x+99y=500

Answer 1

99x + 101y = 499 ------ (1)
101x + 99y = 500 ------(2)
multiplying eqn (1) by 101 and eqn (2) by 99 we get
9999x + 10201y = 50399 -----(3)
9999x + 9801y = 49500 ------(4)
now changing the sign of eqn (4) we get
9999x + 10201y = 50399
-9999x -9801y = -49500
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400y = 899
y = 899/400 = 2.2475
now substituting the value of y in eqn (1) we get
99x + (101*899)/400 = 499
99x + 226.9975 = 499
99x = 499 - 226.9975
99x = 272.0025
x = 272.0025/99
x = 2.7475

Answer 2

99x + 101y = 499 ...(1)
101x + 99y = 500 ...(2)
Multiplying (1) and (2) by 99 and 101 respectively and subtracting (2) from (1)

99*99x + 101*99y = 499*99
101*101x + 99*101y = 500*101
- - -
________________________
99*99x - 101*101x = 499*99 - 500*101
9801x - 10201x = 49401 - 50500
- 400x = -1099
x = 1099/400
x = 2.7475

Now, putting the value of x in (1)
99*2.7475 + 101y = 499
272.0025 + 101y = 499
101y = 499 - 272.0025
y = 127.9975 / 101
y = 1.2673

Hence,
x = 2.7475
y = 1.2673