Systems Involving Nonlinear Systems of Equations

ex.
y = x + 2
x² + y² = 9

Graphing the two equations reveal a circle with radius of 3 and the origin as its center and a line whose x and y intercepts are x = -2 and y = 2.

From the graph, the solutions are the points were the line and the circle intersect, and the intersections occur in two points, therefore there are two solutions to the system.

Solving the system analytically finds the exact intersection points, the substitution method works best,.

y = x + 3
x² + y² = 9

substitute

x² + (x + 3)² = 9
x² + x²+ 6x + 9 = 9
2x² + 6x = 0
2x ( x + 3) = 0

x = 0 or x = -3

substitute the values of x into one of the original equations to find the solution points.

y = x + 3 or y = x + 3
y = 0 + 3 or y = -3 + 3
y = 3 or y = 0

The solution points are {(0,3),(-3,0)}