I am using Hawkes Learning System (8.7 Nonlinear Systems of Equations)and my problem is x^2+y^2=13 and y+7=x^2. The answers I came up with are 2 square root of 3 and 3 for my x's. And I received (5,-4) as the y-coordinates. Is this correct?
since x^2 = y+7,
(y+7) + y^2 = 13
y^2 + y - 6 = 0
(y+3)(y-2) = 0
y = -3 or 2
so, x = ±2 or ±3
the solutions are
(-3,2)(3,2)(2,-3)(-2,-3)
How did you arrive at your results?
To check if your answers are correct, we need to substitute the x-values and y-values into the original equations and see if they satisfy both equations.
First, let's substitute the x-values and y-values you got into the equations:
For x = 2√3 and y = 5:
x² + y² = (2√3)² + 5² = 12 + 25 = 37
y + 7 = 5 + 7 = 12
These values do not satisfy the equations because the left side of the first equation is not equal to the right side, and the second equation is not satisfied.
For x = 3 and y = -4:
x² + y² = 3² + (-4)² = 9 + 16 = 25
y + 7 = -4 + 7 = 3
These values do satisfy the equations because the left side of the first equation is equal to the right side, and the second equation is satisfied.
Therefore, (3, -4) is the correct solution to the system of equations x² + y² = 13 and y + 7 = x².