y=2x x^2+y^2=15 what are the solutions to the nonlinear equations

Question

y=2x x^2+y^2=15 what are the solutions to the nonlinear equations

Answer 1

Whenever you have x = something or y = something, you can substitute that "something" for that "x" or "y", in the other equation.

 

Here, you have y = 2x. In x² + y² = 15, substitute "2x" for every "y":

 

x² + (2x)² = 15

 

Solve for x.

 

x² + 4x² = 15

5x² = 15

x² = 3

x = ± √3 [that's radical 3, if it doesn't display correctly]

 

Now, for each x, try that x in the other equation, which allows you to then solve for y.

 

y = 2x

y = 2(√3)

y = 2√3

[√3, 2√3] Pair off the x and y.

 

y = 2x

y = 2(-√3)
y = -2√3
[-√3, -2√3] Pair off the x and y.

 

The two solutions are (√3, 2√3) and (-√3, -2√3). Check each solution in the system of equations by substituting an x value for x and the CORRESPONDING y value for y, in BOTH equations.

 

With the first solution:

 

y = 2x -> 2√3 = 2(√3)

x² + y² = 15 -> (√3)² + (2√3)² = 15