Systems Of Equations Math Worksheet
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1
2
3Systems of Equations
Anytime we have two or more equations, we have what is called a system of
equations. In our case, we are going to be interested in two linear equations. The
goal of a system of equations is finding the place where the (x, y) value is the
same for both lines, or where the lines cross. One way we can do this is by
graphing.
=
+
+
=
−
=
2
3
2
5
2
3
8
y
x
x
y
x
y
Ex 1:
Ex 2:
Ex 3:
=
+
+
=
−
=
2
2
7
4
6
16
y
x
x
y
x
y
Notice that in example 1, we get two lines that cross at a single point. In example
2, we get two lines that are parallel, and in example 3, we get a single line
because the lines cross everywhere (both lines are the same). These are the three
possibilities with systems of equations. Notice that in the last two examples, both
lines in the system have the same slope. Graphing is a great way to get an idea of
where your lines are going to cross, if at all, but sometimes it can only give us an
estimate and not the exact answer. This happens when the equations cross at
points that are not “nice”.
Substitution
A method called substitution can be used instead of graphing in order to get
a more accurate result. This is best used when one of the coefficients of “x” or “y”
in either equation is “1”. Let’s check out example 1 above using substitution.
=
+
2
3
y
x
Ex 1:
Notice that we have solved for “y” in both equations. While
=
+
2
y
x
doing this in both equations is not necessary, we can use it
to our advantage.
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