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Help finding x and y.

Epitomessence

12

I have two equations involving x and y, and I'm not sure where to go next from my workings:

All help greatly appreciated :smile:

Reply 1

SimonM

18

Hint: Let x+y = a, x-y = b

Reply 2

SumTingWong

14

take out common factors from both equations so you get:

x (1 + y + x) = 9

y (1 + x + y) = -3

Then you can equate both as such:

9/x = -3/y

=> x = -1/3y

Sub that back into the second equation to get y. Then sub that into equation 1 to get x.

Reply 3

Camulodunum

Common geeks, ur great chance to hook up ...

Reply 4

Necro Defain

11

I love your writing :smile:

Can't help you thought since those other 2 posts are already helpful :smile:

Reply 5

SumTingWong

14

Camulodunum

Common geeks, ur great chance to hook up ...

lolwut?

Reply 6

Goldfishy

8

SumTingWong

take out common factors from both equations so you get:

x (1 + y + x) = 9

y (1 + x + y) = -3

Then you can equate both as such:

9/x = -3/y

=> x = -1/3y

Sub that back into the second equation to get y. Then sub that into equation 1 to get x.

This is the way to do it. However it's:

\frac {9}{x} = \frac {-3}{y}

x = -3y

before the subbing in.
I think there are 2 solutions in {x,y}?

Reply 7

Necro Defain

11

An alternative way would be to re-arrange equation two for x, substitute into equation 1 and then solve it as a quadratic (the cubic and quartic terms all cancel) if you find this method easier

Reply 8

Epitomessence

OP

12

Ah, so all my working was on completely the wrong road, fail!!

thanks to everyone for your help, I got it now :smile:

Reply 9

German Jaime

2

x and y are there already why do we need to still find it. ffs

Reply 10

German Jaime

2

x and y are there already why do we need to still find it. ffs

Reply 11

nota bene

15

Epitomessence

Ah, so all my working was on completely the wrong road, fail!!

Not entirely - you can use it if you wish - it's just not the most direct way. I solved it by using your last equation and (x-y)(1+x+y)=12 and then to keep algebra nice sub k=x-y and z=x+y. Solve the quadratic in z that you get from your equation and work with the two solutions from that to find the two ordered pairs (x,y) that solve the question.

Help finding x and y.

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