Solving Systems of Equations
When solving a system of equations, we are trying to find an x and y that will make both
of the equations true. The solution is usually given as an ordered pair (x, y).
2 x  y  3
For example, the solution to the system of equations: 
 is (2,7) because we
 x  2 y  16 
can plug 2 in for x and –7 in for y and get true statements:
2(2)  (7)  3 and
2  2(7)  16 .
In Math 72, we will solve systems of equations by (1) graphing, (2) substitution, and (3)
elimination. This activity will focus on the graphing method.
 y  3x  8 
1. Now consider the system of equations 
 . Use the graph paper below
 y  2 x  2
on the left to graph both lines. Where the lines intersect will be the solution to the
system of equations. Find the solution by finding the point where the two lines
intersect. Give the solution of the system: ( ,
)
y
y
x
x
2. If the equations are not already solved for y, and you want to solve it graphically, you
must first solve each equation for y. Let’s look at the system of equations
6 x  3 y  12


 x  2 y  3 
First solve each equation for y and then graph each equation on the graph paper
above on the right. Give your solution as a coordinate point:
(
,
)
 y  8  2x 
3. a. Graph the following system of equations below on the left. 

 y  2( x  4)
b. Explain what you notice about the lines.
c. What would the solution to this system of equations be? (Remember that the
solution to a system of equations is the point where the graphs intersect.)
y
y
x
 y   x  2
4. a. Graph the following system of equations above on the right. 

y  6  x 
b. Explain what you notice about the lines.
c. What would the solution to this system of equations be? (Remember that the
solution to a system of equations is the point where the graphs intersect.)
x