Lesson 14Solving More Systems
Learning Goal
Let’s solve systems of equations.
Learning Targets
I can use the structure of equations to help me figure out how many solutions a system of equations has.
Lesson Terms
- system of equations
Warm Up: Algebra Talk: Solving Systems Mentally
Problem 1
Solve these without writing anything down:
Activity 1: Challenge Yourself
Problem 1
Here are a lot of systems of equations:
A
B
C
D
E
F
G
H
I
J
K
L
Without solving, identify 3 systems that you think would be the least difficult to solve and 3 systems that you think would be the most difficult to solve. Be prepared to explain your reasoning.
Choose 4 systems to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.
Activity 2: Five Does Not Equal Seven
Problem 1
Tyler was looking at this system of equations:
He said,
“Just looking at the system, I can see it has no solution. If you add two numbers, that sum can’t be equal to two different numbers.”
Do you agree with Tyler?
Are you ready for more?
Problem 1
In rectangle
Lesson Summary
When we have a system of linear equations where one of the equations is of the form
Since we know that
and then solve the equation for
We can find
is the solution to this system. We can verify this by looking at the graphs of the equations in the system:
Sure enough! They intersect at
We didn’t know it at the time, but we were actually using substitution in the last lesson as well. In that lesson, we looked at the system
and we substituted