12x^2 - 5y^2 = 7
2x - 5y = 7
2x = 7 + 5y
(square both sides and expand)
4x^2 = 49 + 70y + 25y^2
(whole eqn multiply by 3)
12x^2 = 147 + 210y + 75y^2
(sub into 1st eqn and simplify)
147 + 210y + 75y^2 - 5y^2 = 7
70y^2 + 210y + 140 = 0
(take out common factor 70)
y^2 + 3y + 2 = 0
(y+1)(y+2) = 0
y = -1 or y = -2
when y = -1,
2x = 7 -5
2x = 2
x = 1
when y = -2
2x = 7 - 10
2x = -3
x = -3/2
solutions -- (1,-1) and (-3/2,-2)
when u substitute u forgot the /2 part. thats y u cant get the same answer as me or fireice. i did u method n i got the same answer. So hard working :D
Hi FireIce,
An excellent tip!
Cheers,
Wen Shih
when u square the fraction both the top n the bottom must be square meaning if (1/2)^2 =1/4
also:24 (5y + 7)^2 - 10y^2 = 14
u didnt sub in the /2
the mistake is here
it is a concept problem, not a working mistake
Sub (1) in (2), 12 (5y/2 + 7/2)^2 - 5y^2 = 7
24 (5y + 7)^2 - 10y^2 = 14
u wanna multiply 2 to get rid of the fraction
but when u multiply 2 to the whole eqn, it only applies to the number in front of the bracket
not in the bracket also
using a simple eqn to illustrate this concept
2(3+5) = 16
when u x2 to both sides,
it will be
(2x2)(3+5) = 2(16) = 32
if using your way, then it becomes
4(6+10)
which is not equal to the other side
12x^2 - 5y^2 = 7------(1)
2x - 5y = 7-------------(2)
x=7+5y/2
sub x=7+5y/2 into (10
12(7+5y/2)^2-5y^2=7
12(49+70y+25y^2/4)-5y^2=7
(588+840y+300y^2/4)-5y^2-7=0
multiply by 4 on both side to get a equation without any fractions involved
588+840y+300y^2-20y^2-28=0
280y^2+840y+560=0
70y^2 + 210y + 140 = 0
(take out common factor 70)
y^2 + 3y + 2 = 0
(y+1)(y+2) = 0
y = -1 or y = -2
when y = -1,
2x = 7 -5
2x = 2
x = 1
when y = -2
2x = 7 - 10
2x = -3
x = -3/2
solutions -- (1,-1) and (-3/2,-2)