Lesson 13Solving Systems of Equations
Learning Goal
Let’s solve systems of equations.
Learning Targets
I can graph a system of equations.
I can solve systems of equations using algebra.
Lesson Terms
- system of equations
Warm Up: True or False: Two Lines
Problem 1
Use the lines to decide whether each statement is true or false. Be prepared to explain your reasoning using the lines.
A solution to
is 2. A solution to
is 8. A solution to
is 8. A solution to
is 2. There are no values of
and that make and true at the same time.
Activity 1: Matching Graphs to Systems
Here are three systems of equations graphed on a coordinate plane:
Problem 1
Match each figure to one of the systems of equations shown here.
Graph A
Graph B
Graph C
Problem 2
Find the solution to each system and then check that your solution is reasonable on the graph.
Notice that the sliders set the values of the coefficient and the constant term in each equation.
Change the sliders to the values of the coefficient and the constant term in the next pair of equations.
Click on the spot where the lines intersect and a labeled point should appear.
Print Version
Find the solution to each system and check that your solution is reasonable based on the graph.
Activity 2: Different Types of Systems
Your teacher will give you a page with some systems of equations.
Problem 1
Graph each system of equations by typing each pair of the equations in the applet, one at a time.
Print Version
Graph each system of equations carefully on the provided coordinate planes.
Problem 2
Describe what the graph of a system of equations looks like when it has …
1 solution
0 solutions
infinitely many solutions
Are you ready for more?
Problem 1
The graphs of the equations
Lesson Summary
Sometimes it is easier to solve a system of equations without having to graph the equations and look for an intersection point. In general, whenever we are solving a system of equations written as
we know that we are looking for a pair of values
For example, look at this system of equations:
Since the
We can solve this equation for
But this is only half of what we are looking for: we know the value for
or
In both cases, we find that
In general, a system of linear equations can have:
No solutions. In this case, the lines that correspond to each equation never intersect.
Exactly one solution. The lines that correspond to each equation intersect in exactly one point.
An infinite number of solutions. The graphs of the two equations are the same line!