Help Me Solve Equationsystem Problem with x & y

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In summary, the conversation is about simplifying equations and finding a formula for x and y in a system of equations with constants a, b, c, d, e, and f. The equations can be graphed as upper hemispheres of circles in the xy-plane and can be solved using geometry instead of algebra.
  • #1
nastyjoe
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My maths skills are so rusty that I can't figure out how I simplify these equations so that I get a formula for x and y... a,b,c,d,e,f are constants

y=[itex]\sqrt{b^{2} - (x-f)^{2}}[/itex] + e
x=[itex]\sqrt{a^{2} - (y-c)^{2}}[/itex] + d

Can anyone help me? And is this equationsystem even possible?
 
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  • #2
If you subtract the constants from both sides and square both sides, you should be able to see that your equations can be graphed in the xy-plane as the upper hemisphere of a circle of radius b centered at (f, e) and the upper hemisphere of a circle of radius a centered at (d, c). Whether these two curve segments intersect or not is up to the values of the constants.
To start, you can just use substitution: substitute your expression for y as a function of x into the second equation.
 
  • #3
I tried substituting y as a function of x into the second equation but I got an awfully complicated equation which I was unable to solve as I'm not that good at maths... :( Are you able to get a solution?
 
  • #4
nastyjoe said:
My maths skills are so rusty that I can't figure out how I simplify these equations so that I get a formula for x and y... a,b,c,d,e,f are constants

y=[itex]\sqrt{b^{2} - (x-f)^{2}}[/itex] + e
x=[itex]\sqrt{a^{2} - (y-c)^{2}}[/itex] + d

Can anyone help me? And is this equationsystem even possible?

nastyjoe said:
I tried substituting y as a function of x into the second equation but I got an awfully complicated equation which I was unable to solve as I'm not that good at maths... :( Are you able to get a solution?

Welcome to the PF.

What are these equations from?
 
  • #5
If you square the first equation, you get
##(y-e)^2 + (x-f)^2 = b^2##

If you draw a graph of that equation, what shape of curve do you get? (If you can't see the answer to that, start with the simpler case when e = f = 0).

The easiest way to solve the two equations is using geometry, not algebra.
 

1. How do I solve an equationsystem problem with x and y?

To solve an equationsystem problem with x and y, you will need to use algebraic methods to isolate one variable in one equation and substitute its value into the other equation. Then, you can solve for the remaining variable.

2. What are the steps for solving an equationsystem problem with x and y?

The steps for solving an equationsystem problem with x and y are as follows:1. Identify the equations and label them as equation 1 and equation 22. Choose a variable (x or y) to eliminate by multiplying one or both equations by a constant3. Add or subtract the equations to eliminate the chosen variable4. Solve the resulting equation for the remaining variable5. Substitute the value of the remaining variable into either equation to solve for the other variable

3. Can I solve an equationsystem problem with x and y using a graph?

Yes, you can solve an equationsystem problem with x and y using a graph. You will need to plot the two equations on the same coordinate plane and find the point of intersection. This point represents the solution to the equationsystem problem.

4. What if I have more than two equations in my equationsystem problem with x and y?

If you have more than two equations in your equationsystem problem with x and y, you can still use the same steps as you would for two equations. You will need to eliminate one variable at a time until you are left with one equation and one variable to solve for.

5. Are there any shortcuts or tricks for solving equationsystem problems with x and y?

Yes, there are some shortcuts or tricks for solving equationsystem problems with x and y. One common method is to use the substitution method, where you solve one equation for one variable and substitute its value into the other equation. Another method is the elimination method, where you add or subtract the equations to eliminate one variable. It can be helpful to practice with different equationsystems to determine which method works best for you.

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