   SEARCH HOME Math Central Quandaries & Queries  Question from james, a student: 3x+2y=9;24x-2y=18 My math teacher says that it is (2,-4) Can someone please explain how to figure this out by graphing? James,

The graph of an equation is the collection of all pairs (x, y) for which the equation is true.
To solve a system of equations you need to find all pairs (x, y) for which all equations in
the system are true. The description of the graph in the first sentence says that these are
the pairs in common to all of the graphs -- the points, if any, where the all of the graphs
cross (at the same time).

You can always check your solutions by plugging the points you get into the equations to
see if they (the points) make the equations true. It doesn't look to me like (2, -4) makes either
3(2) + 2(-4) = 6-8 = -2, not 9; and
24(2) - 2(-4) = 48 + 8 = 56, not 18.

That says that there is a problem somewhere. Either there has been an arithmetic mistake
(easy to do, but one can always check as above) or maybe an error in copying the question
down.

Good luck.
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