Math, Year 10, Simult. Equations

How can i know if two lines/equations intersect on a graph, algebraically? For example, I have two equations:

1. -x^2 + 3x + 4, and
2. x - 4

Ty in advan.

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  1. Equations need an "equal" sign and usually consist of both x and y terms.
    Did you mean y = -x^2 + 3x + 4 and y = x-4 ?

    Make a table of values for each one.
    The first one is a downwards opening parabola, get about 4 or 5 points and you should see the general shape of it.
    The second is a straight line, so you need only 2 points.
    You should see that they intersect at two points

    For an algebraic solution, set the y's equal to each other.
    x-4 = -x^2 + 3x + 4
    x^2 - 2x - 8 = 0
    solve this quadratic, (hint: it factors nicely)

    compare your algebraic answer to your graphic answer, they of course must be the same.

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