Solve for x & y

David Cohen

Take a look at this beauty.

You say?

 

solve for x and y in terms of a,b,c,d,e, and f

ax+by=c
dx+ey=f
-----------------------

ax+by=c...........solve foy x
ax=c-by
x=c/a-by/a
x=(c-by)/a.........eq.1

dx+ey=f.......solve foy x
dx=f-ey
x=f/d-ey/d
x=(f-ey)/d.......eq.2

from eq.1 and eq.2 we have

(c-by)/a=(f-ey)/d......solve foy y
d(c-by)=a(f-ey)
dc-bdy=af-aey
dc-af= bdy-aey
dc-af= y(bd-ae)


go to

x=(c-by)/a.........eq.1, substitute y






........simplify numerator

 

1. Don't you just love David Cohen questions?

2. What is the reason for this exercise?

Throughout my school years, I never had to find x and y for such a problem. Very messy thread. Agree?

 

1. me too

2. this might be good answer

“Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice”
― George Pólya

and

A somewhat advanced society has figured how to package basic knowledge in pill form.
A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available. The pharmacist says "Here's a pill for English literature." The student takes the pill and swallows it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history," replies the pharmacist.
The student asks for these, and swallows them and has new knowledge about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard to swallow."

good to know:

Two is the oddest prime of all prime numbers, because it's the only one that's even!

A mathematician believes nothing until it is proven.
A physicist believes everything until it is proven wrong.

so, solving that kind of problems helps you to develop important skills, like attention to details and

• critical thinking
• problem solving
• analytical thinking
• quantitative reasoning
• ability to manipulate precise and intricate ideas
• construct logical arguments and expose illogical arguments

 

Great reply. Thanks.

 

How I would solve
ax+ by= c
dx+ ey= f.

Multiply each term of the first equation by e to get aex+ bey= ce.
Multiply each term of the second equation by b to get bdx+ bey= fb.
Subtract the second equation from the first, eliminating y: (ae- bd)x= ce- bf.
Divide both sides by ae- bd: x= (ce- bd)/(ce- bf)

To get y, eliminate x: Multiply each term of ax+ by= c by d to get adx+ bdy= cd.
Multiply each term of dx+ ey= f by a to get adx+ aey= af.
Subtracting adx+ aey= af from adx+ bdy= cd to eliminate x: (bd- ae)y= cd- af.
Divide both sides by bd- ae: y= (cd- af)/(bd- ae).

 

Cool.