(1) ax + by = c
(2) dx + ey = f
Ralph is trying to solve the system of equations. He begins
by subtracting ax from both sides of equation (1),
Ralph does this:
(1) ax + by = c
-ax -ax
---------------
by = c-ax
and then he divides the equation by b.
So he does this:
Before he can continue, his friend Alice comes along
and says, "No, you should have subtracted By from both
sides, and then divided by A. You will get the wrong answer.
She is wrong to tell him that he will get the wrong answer,
because he will get the right answer if he substitutes
for y in equation (2) like this:
Then multiply by LCD of b
Get terms in x on the left:
Factor out x on the left:
Divide both sides by (bd-ea)
Now although Alice was wrong to tell Ralph that
he would get the the wrong answer, the way she
said to do it would have been just as good. She
would have gotten the same answer as Ralph. She
would have found x first and y second, whereas
Ralph found y first and x second.
Edwin