math help

how would you work out a question like this

given that: x+y = 5 and that (x+4)(y+4) = 55

find the value of xy

Charlie101998

I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.

Reply 2

Smoky saif

OP

15

Original post by Charlie101998

I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.

okay but I get -y^2 +5y -19. Is that solvable?

Reply 3

DFranklin

18

Original post by Charlie101998

I'd start by expanding the brackets in the second equation. The in the first say x = 5 - y. You can then use that in the second equation to work out the value of y. Using that Value of y, find x in the first equation and check to make sure it works in the second.

In this case, you can expand, and then directly use what you know to get an expression for xy. There should be very little calculation involved.

Reply 4

Nour M.

14

There are two ways of solving this question, with one more complex than the other.

1) Long method involves solving directly for either x or y, then using the value obtained to calculate the other variable, before finally multiplying both values together to find the value of xy. You can use the method of the simultaneous equation for this but as you have probably figured out on your own that that would result in a series of complicated equations. In a previous reply, you said you'd get one equation such as: -y^2 + 5y -19, which is in fact solvable but unfortunately has no real number solutions. However, all of this can be avoided by using the next method.

2) Direct substitution and solving. Since they didn't ask for the exact value of either x or y, I'd suggest you should start looking for ways to directly solve for the expression of xy from what you know. Try to break apart what you've been given and play around with the terms and relate both equations with each other.

Edited for paragraphing

(edited 3 years ago)

Reply 5

DFranklin

18