Solving Ax + By = Cx + Dy: A=C & B=D?

  • Thread starter Thread starter Voivode
  • Start date Start date
AI Thread Summary
In the equation Ax + By = Cx + Dy, whether A = C and B = D depends on the interpretation of the equality sign. If "=" is understood as "identically equal to," then A must equal C and B must equal D for all x and y. However, if "=" is taken as a standard equality, A and C can differ while still satisfying the equation for specific values of x and y. An example illustrates that with specific values, the equation can hold true without A equaling C or B equaling D. Thus, the equality's meaning is crucial to determining the relationship between A, B, C, and D.
Voivode
Messages
19
Reaction score
0

Homework Statement


I'm in a calculus course, but this isn't really a calculus question. I was wondering if:

Ax + By = Cx + Dy

Could I say A = C and B = D?

Homework Equations


None.

The Attempt at a Solution


None.
 
Physics news on Phys.org
Voivode said:

Homework Statement


I'm in a calculus course, but this isn't really a calculus question. I was wondering if:

Ax + By = Cx + Dy

Could I say A = C and B = D?
It depends on what "=" means. In the first equation, if "=" means \equiv (identically equal to), then yes, A = C and B = D. Here, "identically equal to" means for any choice of x and y.

On the other hand, if "=" means just plain old "equals", then no.

Here's an example. Suppose x = 3 and y = 2. Your equation is equivalent to (A - C)x = (D - B)y, so if A = 5 and C = 3, and B = 1 and D = 4, then we have (5 - 3)3 = (4 - 1)2, or 6 = 6, a true statement, but A and C aren't equal, nor are B and D.
 
Last edited:
That makes sense. Thanks.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Similar threads

What Are the Values of A, B, and C for the Given Expression?
Replies
19
Views
3K
Can a Polynomial be Transformed to Eliminate its Quadratic and Linear Terms?
Replies
1
Views
2K
How Do I Solve Linear Equations with Variables and Coefficients?
Replies
36
Views
5K
What Are the Values of c and d for This Precalculus Limit Problem?
Replies
10
Views
2K
Solving these Simultaneous Equations
Replies
3
Views
2K
Does the Pythagorean Identity Hold for sin^2(3x) + cos^2(3x)?
Replies
4
Views
2K
Show that (a-b) + (c-d) = -(b+d) - (-a-c)
Replies
6
Views
1K
Integer solutions to ax^2 + bx - cy^2 - dy = 0
Replies
3
Views
2K
System of Linear Equations - Proving
Replies
2
Views
2K
MHB Prove No Integers Solve $ax^3+bx^2+cx+d=1$ for x=19,2 for x=62
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top