Question

Solve the system numerically.
0.5x-0.1y=0.1
0.1x-0.3y=-0.4

Answer 1

For a start, you can multiple all the terms in both equations times 10, it will look more friendly:

5x-y=1
x-3y=-4 --> x=3y-4


5x-y=1
--> 5(3y-4)-y=1
--> 15y-20-y=1
--> 14y=21
--> y=2

x=3y-4
--> x=3*2-4
--> x=6-4
--> x=2

Answer 2

This system of equations may be solved using either the "substitution" method or the "elimination" method, both will result in a "numerical" solution.

Answer 3

and I made a mistake somewhere above :)

Answer 4

The above by fiddlearound was the substitution method.

Answer 5

fixed version coming :)

Answer 6

And now you have an example of the "elimination" method.

Answer 7

5x-y=1
x-3y=-4 --> x=3y-4

5x-y=1
--> 5(3y-4)-y=1
--> 15y-20-y=1
--> 14y=21
--> y=21/14=3*7/(2*7)=3/2=1.5


x=3y-4
--> x=3*(3/2)-4
--> x=9/2-4
--> x=1/2=0.5

Answer 8

radar, did you mention cramer's method ?
and of course - paying attention needed to avoid stupid mistakes :) ?

Answer 9

Shanna had an error where 14x=7 resulted in 2 instead of correctly 1/2

Answer 10

join my club shanna :)

Answer 11

thank you radar
my mistake

Answer 12

pl let me correct my mistake

Answer 13

Did not mention Cramer's method. Just substitution and elimination methods. Is the Cramer's method a variation of one of those?

Answer 14

http://en.wikipedia.org/wiki/Cramer%27s_rule#Explicit_formulas_for_small_systems

Answer 15

More of a mis-step than a mistake, we knew what you meant to do shanna.

Answer 16

thank you once again

Answer 17

You know I have studied the Cramer's method, but have used it so little that I forgot about it. Probably a system of 3 or more unknowns, it would be more useful than the other two methods.

Answer 18

Thank you everyone. Only took me 3 days to finally figure this out.

Answer 19

Cramer's method is what amistre uses automatically - he has the formula memorized :)
I never remember it.