Solving Systems of Equations
1)
Systems of equations can be solved in several ways.
a)
List the methods that can be used to solve a system of equations.
b)
Which method(s) are you most comfortable with? Why?
c)
Which method(s) are you least comfortable with? Why?
2)
Find an example of a system of equations in your textbook in which the directions tell you to use one method
but you think a different method would be easier. Solve using both methods to show why your choice of
solution method is better.
3)
Look at each system of equations. State the method you would use to solve it and why you chose that method.
You do NOT need to solve the system.
9 x  12y  6
8 x  6y  24
a) 
  x  4 y  7
 2 x  y  7
b) 
y  x  4
3 x  5 y  12
c) 
© 2013 Kathleen Strange
www.mathmadepossible.com
4)
The graph of a system of equations is shown.
a)
What is the solution to the system?
b)
What is the meaning of the solution?
c)
How could you check that your solution is
correct?
5)
Jan says she can solve the system 
 y  4 x  12
using elimination without rearranging any terms. Is this
 y  2x  2
possible? Explain.
6)
Students are trying to explain why the elimination method works when solving systems of equations. One
student wrote, if 5 = 5 and 3 = 3, then 8 = 8. Also, if 5 = 5 and 3 = 3, then 2 = 2.
What is the student’s reasoning?
© 2013 Kathleen Strange
www.mathmadepossible.com
7)
Chris solved a system of equations and got 0 = 4. What can Chris conclude about the system? What can Chris
conclude about the graph of this system? Explain how you know.
8)
Write a system of equations that has infinite solutions. Without solving the system, explain how you know the
system has infinite solutions.
9)
Ian has solved the system 
3 x  2y  12
and explained his method below:
3 x  5 y  18
In moving from the first equation to the second, all that changes is that we're adding 3y on the left side. On the
right side, we add 6. So it must be the case that 3y is the same as 6, which means that y must equal 2. (from Dr.
Math: http://mathforum.org/library/drmath/view/61608.html )
Which algebraic method is Ian using? Explain how you know.
© 2013 Kathleen Strange
www.mathmadepossible.com
10)
11.
The graph of y = x2 +3x + 2 is a parabola. The graph of y = 2x + 4 is a line.
a)
Describe the different ways the line and parabola could intersect. Explain how you know.
b)
Besides graphing, describe the method you would use to find the intersection of the line with the
parabola. Why would you choose that method?
c)
(optional) Use algebra to determine the intersection(s) of the parabola and line.
A student graphed a system of linear equations to find a solution. The student’s response is shown.
Student response: This system has no solution
because the graphs of the lines do not
intersect.
What error did the student make? What might you
say to help the student understand the error and
give the correct response?
© 2013 Kathleen Strange
www.mathmadepossible.com