This is most likely the most disgusting math topic ever, even more so than the dreaded Calculus.  It involves two or more equations and solving for their intersecrtion point or points, because sometimes there are more than one solution.  Here's an example:

Equation 1: 4x² + 8x + 5 - y = 1

Equation 2: 3x² - x + 3 = y + x + 8

1.  Solve for y: 4x² + 8x + 4 = y

                         3x² - 2x - 5 = y

2.  Because each equation equals the same thing (y), they can be set equal to each other.

4x² + 8x + 4 = 3x² - 2x -5

3.  Solve for zero:  x² + 10x + 9 = 0

4.  Solve for x.  In this case we factor:  (x + 9)(x + 1) = 0

                                                       x = -9 OR x = -1

5. Now we have the two x-values.  Plug them into either origonal equation one-by-one to get the corresponding y-value.

3(-9)² - 2(-9) - 5 = y

243 + 18 - 5 = y

256 = y : So one point of intersection is (-9, 256)

Next: 3(-1)² - 2(-1) - 5 = y

3 + 2 - 5 = y

0 = y: So the other point is (-1, 0)

The answer then is {(-9, 256), (-1, 0)}

Another easy way to solve these is to graph them.  All you do in this case is to graph the two equations on the same graph, look at and identify the intersection point(s) and you're done!

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