Question

5/x+y + 18/x-y =7 and 20/x+y - 9/x-y =1 Find X and Y​

Answer 1

Answer:

x + y = 18

x*y = 72

So we need whole number factors of 72 that fulfill those conditions.

Factors of 72:

1, 2, 3, 4, 6, 8, 9, 12, 18, 36, 72

Two of those numbers add up to 18 and multiply to make 72:

12 and 6

Let x = 12 and y = 6

x+y = 18

12+6 = 18

18 = 18

x*y = 72

12*6 = 72

72 = 72

So x = 12 and y = 6. Now substitute in the third equation:

(12)^2 + (6)^2 = 144 + 36 = 180

Incidentally, there is also another way to solve this problem:

x + y = 18

x*y = 72

Solve for x in the first equation:

x = 18-y

Now substitute for x in the second equation:

x*y = 72

y(18-y) = 72

Distribute:

-2y^2+18y = 72

This is a qudratic equation, so we should format it as such. Subtract 72 from both sides:

-2y^2+18y - 72 = 0

Divide the all terms by -2:

y^2–18y+72 = 0

Factor:

(y-12)(y-6) = 0

You can see that there are two solutions here, as is the result of a typical quadratic equation. The solutions are 12 and 6, and both of these satisfy the conditions posed by the original problem.

Answer 2

Answer:

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Step-by-step explanation:

x + y = 18

x*y = 72

So we need whole number factors of 72 that fulfill those conditions.

Factors of 72:

1, 2, 3, 4, 6, 8, 9, 12, 18, 36, 72

Two of those numbers add up to 18 and multiply to make 72:

12 and 6

Let x = 12 and y = 6

x+y = 18

12+6 = 18

18 = 18

x*y = 72

12*6 = 72

72 = 72