Simultaneous Equations - two squared letters

[One Winged Angel]

Sorry if a similar thread has been made already.

I'm really stuck on a simultaneous equation question - one is linear and the other quadratic. I would be able to do it normally, but two letters are squared:

x = 2y - 5 and x (squared) + 3y (squared) = 57

My mocks are next week and I'm kinda worried -_-"
Any help would really be appreciated.

Thank you ^_^

[StuartS]

x = 2y - 5 and x (squared) + 3y (squared) = 57

sub x = 2y - 5 into your other equation wherever you see x

so you then get

(2y-5)^2 +3y^2 = 57

so
(2y-5)(2y-5) +3y^2 = 57

expand the first bracket
4y^2 - 10y -10y +25 + 3y^2 = 57

group together the terms

7y^2 -20y + 25 =57

Subtract 57 from both sides

7y^2 -20y -32 =0
now factorise
(7y + 8 ) ( y - 4) = 0
so 7y+8 =0 or y-4=0

so y=-8/7 or y=4

sub y= -8/7 into x = 2y -5 to get x=2(-8/7) -5 = -83/7

and sub y= 4 into x=2y-5 to get x=2(4) - 5 = 3

Hope that helps

[One Winged Angel]

Thank you so much, I understand it now :D
(At first I had tried doing it like a normal sim. equation and tried squaring the first equation... which obviously didn't work XD)