Question

Find the approximate solution of the given system of equetions.

8x+py=9

 3x-5y=20

Answer 1

(1) 8x+py=9

(2) 3x-5y=20

(3)=5(1)+p(2)=40x+5py+3px-5py=45+20p,

x(40+3p)=45+20p,

x=(20p+45)/(3p+40).

(4)=3(1)-8(2)=24x+3py-24x+40y=27-160,

3py+40y=-133,

y(3p+40)=-133,

y=-133/(3p+40).

These are the exact solutions.

When p=3 we get x=105/49=15/7, which is close to 2; and y=-133/49=-19/7, which is close to -3.

So one example of an approximate solution is x=2 and y=-3 when p=3.

(1) 16-9=7 (2) 6+15=21 which are close to 9 and 20.