Solving Systems by Elimination (Part 2): IM Alg1.2.15
[url=https://im.kendallhunt.com/HS/teachers/1/2/15/preparation.html]“Solving Systems by Elimination (Part 2)”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.2.15 Lesson
- IM Alg1.2.15 Lesson: Solving Systems by Elimination (Part 2)
- Alg1.2.15 Practice
- IM Alg1.2.15 Practice: Solving Systems by Elimination (Part 2)
IM Alg1.2.15 Lesson: Solving Systems by Elimination (Part 2)
Here is an equation: 50+1=51
[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]
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=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.
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]
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\\ 3x -3y &= 3 \end {align} \end {cases}[/math]
Solve each system of equations without graphing and show your reasoning. Then, check your solutions.
[math]\begin {cases} \begin {align}2x + 3y &= 5\\ 2x +4y &= 9 \end {align} \end {cases}[/math]
Solve each system of equations without graphing and show your reasoning. Then, check your solutions.
[math]\begin {cases} \begin {align}2x + 3y &=16\\ 6x -5y &= 20 \end {align} \end {cases}[/math]
This system has three equations:
[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]
IM Alg1.2.15 Practice: Solving Systems by Elimination (Part 2)
Solve this system of linear equations without graphing:
[math]\begin{cases} 5x + 4y = 8 \\ 10x - 4y = 46 \end{cases}[/math][br]
Select all the equations that share a solution with this system of equations.
[math]\begin{cases} 5x + 4y = 24 \\ 2x - 7y =26 \\ \end{cases}[/math]
Students performed in a play on a Friday and a Saturday. For both performances, adult tickets cost a dollars each and student tickets cost s dollars each.
[size=150]On Friday, they sold 125 adult tickets and 65 student tickets, and collected $1,200. On Saturday, they sold 140 adult tickets and 50 student tickets, and collect $1,230.[br]This situation is represented by this system of equations:[/size][br][math]\begin{cases} 125a + 65s = 1,\!200 \\ 140a + 50s = 1,\!230 \\ \end{cases}[/math][br][br]What could the equation [math]265a+115s=2,430[/math] mean in this situation?[br]
The solution to the original system is the pair [math]a=7[/math] and [math]s=5[/math]. Explain why it makes sense that this pair of values is also the solution to the equation [math]265a+115s=2,430[/math].[br]
[size=150]Which statement explains why [math]13x-13y=-26[/math] shares a solution with this system of equations: [/size][br][math]\begin{cases} 10x - 3y = 29 \\ \text -3x + 10y = 55 \\ \end{cases}[/math]
Select all equations that can result from adding these two equations or subtracting one from the other.
[math]\displaystyle \begin{cases} x+y=12 \\ 3x-5y=4 \\ \end{cases}[/math]
Solve each system of equations.
[math]\begin{cases} 7x-12y=180 \\ 7x=84 \\ \end{cases}[/math]
[math]\begin{cases}\text-16y=4x\\ 4x+27y=11\\ \end{cases}[/math]
Here is a system of equations:
[math]\begin{cases} 7x -4y= \text-11 \\ \text 7x+ 4y= \text-59 \\ \end{cases}[/math][br][br]Would you rather use subtraction or addition to solve the system? Explain your reasoning.
The box plot represents the distribution of the number of free throws that 20 students made out of 10 attempts.
[size=150][img]data:image/png;base64,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[/img][br][br]After reviewing the data, the value recorded as 1 is determined to have been an error. The box plot represents the distribution of the same data set, but with the minimum, 1, removed.[br][img]data:image/png;base64,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[/img][br][br]The median is 6 free throws for both plots.[/size][br][br]Explain why the median remains the same when 1 was removed from the data set.[br]
When 1 is removed from the data set, does the mean remain the same? Explain your reasoning.[br]
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp.
[size=150]One equation that models the relationship between chirps and outdoor temperature is [math]f=\frac{1}{4}c+40[/math], where [math]c[/math] is the number of chirps per minute and [math]f[/math] is the temperature in degrees Fahrenheit.[/size][br][br]Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature?[br]
If it is [math]75^{\circ}F[/math] outside, about how many chirps can we expect to hear in one minute?[br]
The equation is only a good model of the relationship when the outdoor temperature is at least [math]55^{\circ}F[/math]. (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?[br]
On the coordinate plane, draw a graph that represents the relationship between the number of chirps and the temperature.
Explain what the coefficient [math]\frac{1}{4}[/math] in the equation tells us about the relationship.[br]
Explain what the 40 in the equation tells us about the relationship. [br]