Solving Non linear Equations
Example1
2y-3x=1 ------ (1)
y+9x2=8 ------ (2)
from (1) y=(4x+1)/2 ----(3)
sub(1) into (3): (4x+1)/2 + 9x2 - 8 =0
x 2 3x+1+18x2
-16=0
18x2-15+3x=0
(18x-15)(x+1)=0
18x-15=0 or x+1=0
18x=15 x=-1
x=15/18
find y
Example 2
3x/y-2y/x=1 --------- (1)
5x-3y=12 ---------
(2)
(2): x=(12+3y)/5 ----------(3)
multiply (1) by xy
3x2 -2y2=xy ------------(4)
sub (3) into (4)
3(12+3y)
2/5 2 -2y2=y(12+3y)/5
multiply by 25
3(12+3y) 2 -50
y2=5y(12+3y)
3(144+72y+9y2)-50
y2=60y+15y2
432+216y+27y2
-50y2 -60y-15y2 =0
-38y2-60y+432=0
19y2 +30y-216=0
(19y+36)(y-6)=0
y=-36/19 or y=6
find x
<Equations>
tags