Question

Check my work for errors.

Answer 1

If 4x + 3y = 18xy and 2x - 5y + 4xy = 0, then what are the values of x and y respectively?

Answer 2

This is what I did please check it:
4x + 3y = 18xy
4x + 3y - 18xy = 0----(1)
2x - 5y + 4xy = 0 -----(2)
Multiply (2) by -2,
-4x +10y - 8xy = 0------(3)
4x + 3y - 18xy = 0 -----(1)
Adding (3) and (1),
13y - 26xy = 0
y(13 - 26x) = 0
Either y = 0 or 13 - 26x = 0.
But y cannot be 0, which is clear from (1).
Therefore, 13 - 26x = 0, -26x = -13, x=-13/-26 = 1/2
Substituting this value in (1),
4(1/2) + 3y -18(1/2)y = 0
2 + 3y -9y = 0
-6y = -2, y = -2/-6 = 1/3.
hence the values of x and y are 1/2 and 1/3 respectively.

Answer 3

This is how you can check your own work:
plug both x and y into both equations, and make sure the results are correct

Answer 4

i.e.:
is 4 * (1/2) + 3 * (1/3) equal to 18 * (1/2) * (1/3) ?

Answer 5

The numbers have to work for both equations

Answer 6

Can you show me how to do that exactly?

Answer 7

4 * (1/2) + 3 * (1/3) = 18 * (1/2) * (1/3)
2 + 1 = 9 * (1/3)
3 = 3
This equation looks correct, now do the same for the other one

Answer 8

Thanks!