[math]\begin{cases} 3x-y=17 \\ x+4y=10 \\ \end{cases}[/math][br][br]Solve the system by graphing the equations (by hand or using technology).[br]

Explain how you could tell, without graphing, that there is only one solution to the system.[br]

[math]\begin{cases} y = \frac45x - 3 \\ y = \frac45x + 1 \end{cases}[/math][br][br]Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning.

Try solving the system of equations algebraically and describe the result that you get. Does it match your prediction?[br]

[math]\displaystyle \begin{cases} 9x-3y=\text-6\\ 5y=15x+10\\ \end{cases}[/math]

[size=150]Select [b]all [/b]systems that have no solutions.[/size]

[math]\begin{cases} 2v+6w=\text-36 \\ 5v+2w=1 \end{cases}[/math]

[math]\begin{cases} 6t-9u=10 \\ 2t+3u=4 \\ \end{cases}[/math]

[size=150]Select [b]all [/b]the dot plots that appear to contain outliers.[/size]

[math]\begin{cases} \text-x + 6y= 9 \\ x+ 6y= \text-3 \\ \end{cases}[/math][br][br]Would you rather use subtraction or addition to solve the system? Explain your reasoning.

[math]\begin{cases} 6x-y=18 \\ 4x+2y=26 \\ \end{cases}[/math][br][br]Select [b]all [/b]the steps that would help to eliminate a variable and enable solving.

[math]\begin {cases} \begin{align} 2x+2y&=180\\0.1x+7y&=\hspace{2mm}78\end{align}\end{cases}[/math][br][br][size=150]Here are some equivalent systems. Each one is a step in solving the original system.[/size][br][br][table][tr][td]Step 1:[/td][td]Step 2:[/td][td]Step 3:[/td][/tr][tr][td][math]\begin {cases} \begin{align} 7x+7y&=630\\0.1x+7y&=\hspace{2mm}78\end{align}\end{cases}[/math][/td][td][math]\begin {cases} \begin{align} 6.9x &=552\\0.1x+7y&=\hspace{2mm}78\end{align}\end{cases}[/math][/td][td][math]\begin {cases} \begin{align} x&=80\\0.1x+7y&=78\end{align}\end{cases}[/math][/td][/tr][/table][br][br][size=150]Look at the original system and the system in Step 1.[/size][br]What was done to the original system to get the system in Step 1?[br]

Explain why the system in Step 1 shares a solution with the original system.[br]

[size=150]Look at the system in Step 1 and the system in Step 2.[br][/size][br]What was done to the system in Step 1 to get the system in Step 2?[br]

Explain why the system in Step 2 shares a solution with that in Step 1.[br]

What is the solution to the original system?[br]