Simultaneous Linear and Non-Linear Equations in Two Unknowns

Daisuke-kun SG

nid help Crying or Very sad

1) 3s^2 + 2t^2 =11
3s + 2t = 1

2) 3x - 2y = 1
(x-2)^2 + (2y+3)^2 = 26

3) 3y - x = 3
2/3y - 1/x = 2

4) find the coordinates of the points where the line 2x+5y+4=0 intersects the curve 2xy = -1

5) The curve xy + 20 = 5x and the line 2y = x-3 intersects at points A and B.
Calculate the coordinate of A and B

Workings might help.
so damn difficult.
i can do other questions except tis...

FireIce SG

use substitution

lpx88 SG

Qn 5 seems damn familiar. TYS qn ah Laughing Aiya all sub in la

eagle SG

I'm going out, so I shall do question 4 and 5 first. 1,2,3 use substitution, similar to what I am going to do for 4 and 5

4)
2xy = -1
x = -1/2y

2x + 5y + 4 = 0
Sub x = -1/2y
-1/y + 5y + 4 = 0
5y^2 + 4y - 1 = 0
(5y - 1) (y + 1) = 0
y = 1/5 or y = -1
x = -5/2 or -1/2

5) 2y = x - 3

xy + 20 = 5x
2xy + 40 = 10x
Sub 2y = x - 3
x(x-3) + 40 = 10x
x^2 -13x + 40 = 0
(x-5) (x-8 ) = 0
x = 5 or 8
y = 1 or 2.5

Daisuke-kun SG

thx eagle.
question 4.
ur ans.
the -1/2 is actually 1/2

but i'm stuck with 1 & 3 Crying or Very sad

eagle SG

yup yup, typo...

eagle SG

1)
3s = 1 -2t

3s^2 + 2t^2 = 11
9s^2 + 6t^2 = 33
Sub 3s = 1 -2t
(1-2t)^2 + 6t^2 = 33
Should be able to solve from here

3)
x = 3y - 3 => Use this in your substitution

is 2/3y same as 2 / (3y) or is it (2/3) y?