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Unformatted text preview: ust have at least
one variable in it.
Also, the system is called linear if the variables are only to the first power, are only in the
numerator and there are no products of variables in any of the equations.
Here is an example of a system with numbers. 3x - y = 7
2x + 3 y = 1 Before we discuss how to solve systems we should first talk about just what a solution to a
system of equations is. A solution to a system of equations is a value of x and a value of y that,
when substituted into the equations, satisfies both equations at the same time.
For the example above x = 2 and y = -1 is a solution to the system. This is easy enough to
check. 3 ( 2 ) - ( -1) = 7
2 ( 2 ) + 3 ( -1) = 1
So, sure enough that pair of numbers is a solution to the system. Do not worry about how we got
these values. This will be the very first system that we solve when we get into examples.
Note that it is important that the pair of numbers satisfy both equations. For instance x = 1 and
y = -4 will satisfy the first equation, but not the second and so isn’t a solution to the...
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- Spring '12