Finding the Solution to xy = x/y = x-y When y ≠ 0

  • Context: High School 
  • Thread starter Thread starter Zeteg
  • Start date Start date
  • Tags Tags
    Strange
Click For Summary
SUMMARY

The equation xy = x/y = x - y, with the constraint that y ≠ 0, leads to the solution where x = -1/2 and y = -1. This conclusion is reached by verifying that substituting these values satisfies both parts of the equation. Specifically, the calculations confirm that y can be either +1 or -1, and the subtraction yields consistent results. The analysis demonstrates the interrelation of the variables in the equation.

PREREQUISITES
  • Understanding of algebraic equations and manipulation
  • Familiarity with solving simultaneous equations
  • Knowledge of the properties of fractions
  • Basic skills in mathematical verification
NEXT STEPS
  • Explore advanced algebraic techniques for solving non-linear equations
  • Learn about the implications of variable constraints in equations
  • Study the graphical representation of equations to visualize solutions
  • Investigate the use of mathematical software for solving complex equations
USEFUL FOR

Students, mathematicians, and anyone interested in solving algebraic equations and understanding variable relationships in mathematical contexts.

Zeteg
Messages
85
Reaction score
0
One of my friends asked me this, and I have no idea how to get the answer. I don't even know if there is an answer... if someone could help, that'd be great:

xy = x/y = x-y

If y cannot equal 0, what is the value of x and y?

Thanks :D
 
Mathematics news on Phys.org
Unless I goofed in the calculation, x is -1/2 and y is -1. Work out xy = x/y to see that y is either +1 or -1, then work out the subtraction.
 
Wow, it works! Thanks =)
 

Similar threads

MHB Integer Solutions for $4x+y+4\sqrt{xy}-28\sqrt{x}-14\sqrt{y}+48=0$
  • · Replies 1 ·
Replies
1
Views
1K
High School Adding 'x' to 'xy' for Resultant <=1: A Table Guide
  • · Replies 18 ·
Replies
18
Views
2K
MHB Positive Integer Solutions of $(x^2+y^2)^n=(xy)^{2014}$
  • · Replies 2 ·
Replies
2
Views
2K
MHB Given f(xy) = f(x)/y and f(500) = 3, find f(600)
  • · Replies 2 ·
Replies
2
Views
3K
MHB Find the minimum of x+y+xy and x+y-xy
  • · Replies 10 ·
Replies
10
Views
3K
Prove if ##x<0## and ##y<z## then ##xy>xz## (Rudin)
  • · Replies 2 ·
Replies
2
Views
2K
MHB Find Min of $\frac{a(x^2+y^2+z^2)+9xyz}{xy+yz+zx}$ for $x+y+z=1$
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Rodrigues' Formula for Laguerre equation
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find the value of x square + y square
  • · Replies 2 ·
Replies
2
Views
15K
High School Calculating the perfect tennis shot using vectors
  • · Replies 2 ·
Replies
2
Views
2K