Systems of Equations: Compare and Contrast
Small Group Directions
- Solve your assigned system of equations using any algebraic method. Show you work and be ready to explain how you solved it.
- Also graph the system of equations and show how the solution appears on your graph. You may use graphing technology such as Desmos.
Group Roles
Facilitator: Read the directions out loud and check whether everyone understands each other.
“How should we start?” “How do you know?”
Team Captain: Help your team members step up and step back.
“How do you know?” “What do you think?”
Resource Manager: Help your group get unstuck.
“Is this working?” “What else could we try?” “Should we ask a team question?”
Recorder/Reporter: Be prepared to share out in the whole class discussion.
“How should I explain...?”
Problems
- \[y=-3x\\4x+y=2\]
- \[y=7x-5\\2x+y=13\]
- \[x=-5y-4\\x-4y=23\]
- \[x+y=10\\y=x-4\]
- \[y=5-x\\4x+2y=10\]
- \[3x+5y=23\\y=x+3\]
- \[y=-x-2\\2x+3y=-9\]
- \[y=2x-3\\-2x+y=1\]
- \[x=\frac{1}{2}y+\frac{1}{2}\\2x+y=-1\]
- \[a=2b+4\\b-2a=16\]
- \[y=3-2x\\4x+2y=6\]
- \[y=x+1\\x-y=1\]
(Adapted from CPM Core Connections)
Whole Class Directions
- Each group will share out how you solved your system of equations.
- Listen to each group and think about similarities and differences.
- Ask questions about anything you do not understand or you disagree with.
- You do not need to write anything during the whole class discussion, but you will have an exit ticket to see what you learned from the discussion.
Exit Ticket: Systems of Equations Compare and Contrast
Sheila missed class today. She tried to solve Problem 8 on her own, but she thinks she made a mistake because -3 does not equal 1.
\begin{align}
&y=2x-3\\
&-2x+y=1
\end{align}
\begin{align}
&-2x+(2x-3)=1\\
&-2x+2x-3=1\\
&0-3=1\\
&-3=1
\end{align}
Explain to Sheila what happened, using as much detail as possible to help her understand this type of problem.