Chapter 1.2 Solving Non linear Equations

Chapter 1.2

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

                  

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