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

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In summary, the equation "xy = x/y = x-y" is a system of equations with three variables that can be solved using algebraic manipulation and substitution. There are infinitely many solutions, but certain restrictions may apply depending on the context of the problem. The equation can also be graphed, but the shape of the graph will vary depending on the values of x and y. The restriction y ≠ 0 is necessary for the equations to have a valid solution, as dividing by 0 is undefined in math.
  • #1
Zeteg
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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
 
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  • #2
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.
 
  • #3
Wow, it works! Thanks =)
 

1. What does the equation "xy = x/y = x-y" mean?

The equation "xy = x/y = x-y" is a system of equations that involves three variables: x, y, and z. The first equation, "xy = x/y", means that the product of x and y is equal to the quotient of x and y. The second equation, "x/y = x-y", means that the quotient of x and y is equal to the difference between x and y. This system of equations is only valid when y is not equal to 0.

2. How do you solve for x and y in this equation?

To solve for x and y in this equation, you can use algebraic manipulation and substitution. First, rearrange the equations to isolate one variable, for example, x in the first equation. Then, substitute the expression for x into the other equations to solve for y. Repeat the process for the other variable.

3. What are the possible solutions for this equation?

There are infinitely many solutions to this equation, as it is a system of equations with two variables. However, there may be restrictions on the values of x and y depending on the context of the problem. For example, if the equation represents a real-life scenario, the solutions may be limited to positive or negative numbers, or within a certain range.

4. Can you graph this equation?

Yes, this equation can be graphed on a coordinate plane. However, since it is a system of equations with two variables, the graph will be a straight line or a curve, rather than a single point. The shape of the graph will depend on the specific values of x and y that satisfy the equations.

5. Why is the restriction y ≠ 0 necessary in this equation?

The restriction y ≠ 0 is necessary because if y were equal to 0, the equations would become undefined. In the first equation, the denominator would be 0, which is not allowed in math. In the second equation, dividing by 0 would also result in an undefined value. Therefore, y must be a non-zero value for the equations to have a valid solution.

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