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Lesson 20
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
Lesson 20A: Solution Sets to Equations with Two Variables
Classwork
Exercise 1
a.
b.
Circle all the ordered pairs (𝑥, 𝑦) that are solutions to the equation 4𝑥 − 𝑦 = 10.
(3,2)
(2, 3)
(−1, −14)
(0,0)
(1, −6)
(5,10)
(0, −10)
(3,4)
(6,0)
(4, −1)
How did you decide whether or not an ordered pair was a solution to the equation?
Exercise 2
a. Now, find 5 more solutions to the equation 4𝑥 − 𝑦 = 10 where one or more variables
are negative numbers or non-integer values. Be prepared to share the strategies you used to find your
solutions.
b. Create a visual representation of the solution set by plotting each
solution as a point (𝑥, 𝑦) in the coordinate plane.
c. How many ordered pairs (𝑥, 𝑦) will be in the solution set of the
equation 4𝑥 − 𝑦 = 10?
d. Why does it make sense to represent the solution to the equation
4𝑥 − 𝑦 = 10 as a line in the coordinate plane?
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Solution Sets to Equations with Two Variables
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Lesson 20
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M1
ALGEBRA I
Exercises 3–5
3a. The sum of two numbers is 15. What are the numbers?
b. Create an equation using two variables to represent this
situation. Be sure to explain the meaning of each variable.
c. List at least 6 solutions to the equation you created in part (a).
d. Create a graph that represents the solution set to the equation.
4a. Gia had 15 songs in a playlist composed of songs from her two favorite artists, Beyonce and Jennifer
Lopez. How many songs did she have by each one in the playlist?
b. Create an equation using two variables to represent this situation.
Be sure to explain the meaning of each variable.
c. List at least 3 solutions to the equation you created in part (a).
d. Create a graph that represents the solution set to the equation.
5. Compare your solutions to Exercises 3 and 4. How are they alike? How are they different?
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Solution Sets to Equations with Two Variables
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Lesson 20
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
Exercises 6-9
Sometimes it is helpful to first rewrite an equation by solving for y.
Solve each of the following for y.
6. x + y = 4
7. 3x – 5y = 15
8. 4(y – 2x) = 12
9.
3y + 2x = 10
Choose five values for the domain(x) and make a table.
Domain
x
Range
y
Ordered Pair
(x, y)
Lesson Summary
An ordered pair is a solution to a two variable equation when each number substituted into its corresponding
variable makes the equation a true number sentence. All of the solutions to a two variable equation are called the
solution set.
Each ordered pair of numbers in the solution set of the equation corresponds to a point on the coordinate plane.
The set of all such points in the coordinate plane is called the graph of the equation.
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Solution Sets to Equations with Two Variables
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Lesson 20
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M1
ALGEBRA I
Problem Set 20A
1. Graph the solution set in the coordinate plane.
Label at least two ordered pairs that are solutions on your graph.
a. 10𝑥 + 6𝑦 = 100
x
y
Ordered Pair
(x, y)
y
Ordered Pair
(x, y)
b. 𝑦 = 4(𝑥 + 1)
x
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Lesson 20
M1
ALGEBRA I
c. 𝑦 − 5𝑥 = 2
x
y
Ordered Pair
(x, y)
y
Ordered Pair
(x, y)
d. 7𝑥 − 3𝑦 = 21
x
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Solution Sets to Equations with Two Variables
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Lesson #:
Lesson Description
© 2013 Common Core, Inc. Some rights reserved.
commoncore.org 4/30/17
Date:
Lesson 20
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
2. Mari and Lori are starting a business to make gourmet coffee. They gather the following information from another
business about prices for different amounts of coffee. Which equation and which graph are most likely to model the
price p for 𝑥 pounds of coffee? Justify your reasoning.
Graph 1
Pounds
𝑥
Price 𝑝 for
𝑥 pounds
0.25
$3.6
0.81
$6.48
1
$7.2
1.44
$8.64
Graph 2
Equation A: 𝑝 = 5𝑥 + 2.2
Equation B: 𝑝 = 7.2√𝑥
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Solution Sets to Equations with Two Variables
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Lesson 20
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M1
ALGEBRA I
Lesson 20B: Solution Sets to Equations with Two Variables
Slope-Intercept Form
A linear equation expressed in the form
y = mx + b
m is the slope
b is the y-intercept (where it crosses the y-axis)
Write an equation of the line in slope-intercept form.
a. The slope is 2 and y-intercept is 3.
b. The slope is –2; the y-intercept is 5.
c. The slope is ½; the y-intercept is -4.
d. The slope is 0; the y-intercept is 2.
e. Find the slope and y-intercept of
y = 3x + 2.
g. Find the slope and y-intercept of
x + y = 4.
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f. Find the slope and y-intercept of
y = ⅓x.
h. Find the slope and y-intercept of
6x + 3y = 9.
Solution Sets to Equations with Two Variables
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M1
ALGEBRA I
Graphing Lines Using Slope-Intercept Form
Find the slope and y-intercept
Plot the point (0, b) y-intercept
Use the slope to locate a second point.
Draw a line through the two points.
Graph the following equations using the slope-intercept form.
y = -2x + 3
y – 4x = -5
y = -2 x + 2
3
y= 1x
2
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y=6
x=6
Solution Sets to Equations with Two Variables
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Lesson 20
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
Problem Set 20B
1.
Match each equation with its graph. Explain your reasoning.
a.
𝑦 = 5𝑥 − 6
2
1
b.
𝑥 + 2𝑦 = −12
c.
2𝑥 + 𝑦 = 4
d.
𝑦 = 3𝑥 − 6
e.
𝑥 = −𝑦 − 4
3
4
5
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Solution Sets to Equations with Two Variables
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