Math puzzle: (X.6)(y.4) = 288, X^2-y^2 = -5, X.7-3.x = 19, (Y-x)/(x-y)= -1

Ramyana

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Sep 17, 2017
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Hi
I am trying to solve the following puzzle.
I am struggling with this puzzle along with my kid, who's in algebra class. The conditions are:
1. (X.6)(y.4) = 288
2. X^2-y^2 = -5
3. X.7-3.x = 19
4. (Y-x)/(x-y)= -1
​​​​​​​x and y has to be the same numbers throughout the 4 given conditions.

Thank you
 
You'll have to explain what "x.6" means. Is it an exponent? x^6 or \(\displaystyle x^{6}\)?
 
Hi
I am trying to solve the following puzzle.
I am struggling with this puzzle along with my kid, who's in algebra class. The conditions are:
1. (X.6)(y.4) = 288
2. X^2-y^2 = -5
3. X.7-3.x = 19
4. (Y-x)/(x-y)= -1
​​​​​​​x and y has to be the same numbers throughout the 4 given conditions.

Thank you
Are x & X referring to the same number?

Are y & Y referring to the same number?
 
Thank you for clarifying, but your next step is to show us your work.
 
Thank you for clarifying, but your next step is to show us your work.

I got 19/4 for x and 21/4 for y, using the second and third equation which works perfectly well for all the equations except for equation #1. If I solve for y using equation #1, then it doesn't fit the second equation.
 
That's what I thought too. But the teacher insists that there is a solution.
 
It's not quite redundant. It adds \(\displaystyle \text{Tria}\text{ngle} \ne \text{Square}\).
 
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I figured out the solution by graphing, there is no solution to these set of equations.
 
1. 6x * 4y = 288

2. x^2 - y^2 = 143

3. 7x - 3x =
48

4. (y - x) / (x - y) = -1
This has a nicer solution. ;)


We can make as many solvable systems as we like, by changing the right-hand side of the second and third equations. Pick a number for x (not zero).

x^2 - y^2 = (x^4 - 144)/x^2

7x - 3x = 4x

The solution will be:

x = x (the number you picked)

y = 12/x
 
This has a nicer solution. ;)


We can make as many solvable systems as we like, by changing the right-hand side of the second and third equations. Pick a number for x (not zero).

x^2 - y^2 = (x^4 - 144)/x^2

7x - 3x = 4x

The solution will be:

x = x (the number you picked)

y = 12/x
nice, but according to her, we are not allowed to change stuff.
 
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