Lesson 9: Solving Systems by Elimination (Alg1.2.15)

[size=200][b][color=#0000ff][icon]/images/ggb/toolbar/mode_copyvisualstyle.png[/icon]Classroom Supplies[/color][/b][/size]
A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495.
[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=200][b][color=#0000ff][icon]/images/ggb/toolbar/mode_zoom.png[/icon]A Bunch of Systems[/color][/b][/size]
Solve each system of equations without graphing and show your reasoning. Then, check your solutions.
[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]
[size=200][b][color=#0000ff][icon]/images/ggb/toolbar/mode_zoom.png[/icon]Are you ready for more?[/color][/b][/size]
This system has three equations: [br][math]\begin{cases}3 x + 2y - z = 7 \\ \text{-} 3x + y +2z =\text- 14 \\ 3x+y-z=10 \end{cases}[/math][br][list][*]Use the elimination method in the first two equations to get a new equation.[/*][*]Use the elimination method in the second two equations to get a new equation.[/*][*]Solve the system of your two new equations.[/*][*]Substitute to get all the variables.[/*][/list][list][/list]What is the solution to the original system of equations?[br]
Close

Information: Lesson 9: Solving Systems by Elimination (Alg1.2.15)