Solve the System...2

[nycmathguy]

David Cohen questions just for fun.
Enjoy.

 

[MathLover1]

sqrt(2)x -sqrt(3)y=sqrt(3)..........1)
sqrt(3)x -sqrt(8)y=sqrt(2)............2)
__________________________

sqrt(2)x -sqrt(3)y=sqrt(3)..........1), solve for y

sqrt(2)x -sqrt(3)=sqrt(3)y

sqrt(2)x/sqrt(3) -sqrt(3)/sqrt(3)=y

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

y=(sqrt(2)/sqrt(3))*x -1...............1a)

go to

sqrt(3)x -sqrt(8)y=sqrt(2)............2), substitute y

sqrt(3)x -2sqrt(2)((sqrt(2)/sqrt(3))*x -1)=sqrt(2)........ solve for x

sqrt(3)x -(2sqrt(2)sqrt(2)/sqrt(3)))x =sqrt(2)-2sqrt(2)

sqrt(3)x -(4/sqrt(3)))x =-sqrt(2)

(sqrt(3) -4/sqrt(3))x =-sqrt(2)

(-sqrt(3)/3)x =-sqrt(2)

x =-sqrt(2)/(-sqrt(3)/3)

x =sqrt(6)

go to

y=(sqrt(2)/sqrt(3))*x -1...............1a), substitute x

y=(sqrt(2)/sqrt(3))*sqrt(6) -1

y=2-1

y=1

 

[nycmathguy]

sqrt(2)x -sqrt(3)y=sqrt(3)..........1)
sqrt(3)x -sqrt(8)y=sqrt(2)............2)
__________________________

sqrt(2)x -sqrt(3)y=sqrt(3)..........1), solve for y

sqrt(2)x -sqrt(3)=sqrt(3)y

sqrt(2)x/sqrt(3) -sqrt(3)/sqrt(3)=y

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

y=(sqrt(2)/sqrt(3))*x -1...............1a)

go to

sqrt(3)x -sqrt(8)y=sqrt(2)............2), substitute y

sqrt(3)x -2sqrt(2)((sqrt(2)/sqrt(3))*x -1)=sqrt(2)........ solve for x

sqrt(3)x -(2sqrt(2)sqrt(2)/sqrt(3)))x =sqrt(2)-2sqrt(2)

sqrt(3)x -(4/sqrt(3)))x =-sqrt(2)

(sqrt(3) -4/sqrt(3))x =-sqrt(2)

(-sqrt(3)/3)x =-sqrt(2)

x =-sqrt(2)/(-sqrt(3)/3)

x =sqrt(6)

go to

y=(sqrt(2)/sqrt(3))*x -1...............1a), substitute x

y=(sqrt(2)/sqrt(3))*sqrt(6) -1

y=2-1

y=1

The David Cohen textbook is pretty cool, right?

How about this one?

Difference Quotient