Question

solve 101x+99y=499;99x+101y=501 by elimination method.please answer my question as fast you can.​

Answer 1

Answer:

x = 2 and y = 3

Step-by-step explanation:

101x + 99y = 499    .....(1)

99x + 101y = 501   ......(2)

Add (1) & (2) ==>  200x + 200y = 1000  (Divide by 200) ==> x + y = 5  ...(3)

Subtract (1)-(2)==> 2x - 2y = -2 (Divide by 2) ==> x - y = -1 ....(4)

Add (3) & (4) ===> 2x = 4  ==> x = 2 and y = 3 (sub x =2 in (3) )

Answer 2

Answer: x = 2 and y = 3

Step-by-step explanation:

Given, that ,

101x + 99y = 499  .......................(1)

99x + 101y = 501   .......................(2)

Solving these two equations directly, using elimination method, is not a clever way.

(1) + (2)

ie, 101x + 99y + 99x + 101y = 499 + 501

ie, 200x + 200y = 1000

÷ing by 200, we get,

x + y = 5  .......................................(3)

(1) - (2)

ie, 101x + 99y - (99x + 101y) = 499 - 501

ie, 101x + 99y - 99x - 101y = -2

ie, 2x - 2y = -2

÷ing by 2 , we get,

x - y = -1  .......................................(4)

Now applying elimination method to (3) and (4)

Adding (3) and (4)

x + y + x - y = 5 + -1

2x = 4  ,or, x = 2

substituting x = 2 in (3)

ie, 2 + y = 5

ie,  y = 3

hope this helps.....