[size=150]Perform each of the following operations and answer these questions: What does each resulting equation look like? Is it still a true equation?[/size][br][br]Add 12 to each side of the equation.[br]
Add [math]10+2[/math] to the left side of the equation and 12 to the right side.[br]
Add the equation [math]4+3=7[/math] to the equation [math]50+1=51[/math].[br]
[size=150]Write a new equation that, when added to [math]51+1=51[/math], gives a sum that is also a true equation.[/size][br]
Write a new equation that, when added to [math]50+1=51[/math], gives a sum that is a false equation.[br]
[size=150]Later, she realized that she didn’t order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measuring tape and paid $178.50. [br][br]This system represents the constraints in this situation:[br][math]\begin{cases} \begin {align}20c + 10m &= 495\\ 8c + \hspace{4.5mm} m &= 178.50 \end{align}\end{cases}[/math][br][br]Discuss with a partner:[/size][list=1][*]In this situation, what do the solutions to the first equation mean? [/*][*]What do the solutions to the second equation mean?[/*][*]For each equation, how many possible solutions are there? Explain how you know.[/*][*]In this situation, what does the solution to the system mean?[/*][/list]
[size=150]Find the solution to the system. Explain or show your reasoning.[/size][br]
[size=150]To be reimbursed for the cost of the supplies, the teacher recorded: “Items purchased: 28 calculators and 11 measuring tapes. Amount: $673.50.” [br][br][/size][size=100]Write an equation to represent the relationship between the numbers of calculators and measuring tapes, the prices of those supplies, and the total amount spent.[/size]
How is this equation related to the first two equations?[br]
In this situation, what do the solutions of this equation mean?[br]
How many possible solutions does this equation have?
How many solutions make sense in this situation? Explain your reasoning.
[math]\begin {cases} \begin {align}2x + 3y &= \hspace {2mm}7\\ \text-2x +4y &= 14 \end {align} \end {cases}[/math]
[math]\begin {cases} \begin {align}2x + 3y &= \hspace {2mm}7\\ 3x -3y &= 3 \end {align} \end {cases}[/math]
[math]\begin {cases} \begin {align}2x + 3y &= 5\\ 2x +4y &= 9 \end {align} \end {cases}[/math]
[math]\begin {cases} \begin {align}2x + 3y &=16\\ 6x -5y &= 20 \end {align} \end {cases}[/math]
[math]\begin{cases}3 x + 2y - z = 7 \\ \text{-} 3x + y +2z =\text- 14 \\ 3x+y-z=10 \end{cases}[/math][br][list][*]Add the first two equations to get a new equation.[/*][*]Add the second two equations to get a new equation.[/*][*]Solve the system of your two new equations.[/*][/list][list][/list]What is the solution to the original system of equations?[br]