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Creating Equations: Solving Two Variable Equations
Name: ____TEACHER COPY ______ _______
CCSS.Math.Content.HSA.CED.A.2
Date: ______________________ Period: _____
Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
Lesson on Solving Equations:
1. Warmup (last page)
2. Intro: Solving equations is all about keeping things balanced. Who here has been on a see-saw? What
happens if the person on the other side of the see-saw is much lighter or tinier than you? What happens when
they are much bigger? What happens when you weigh the same? To keep an equation (balanced see-saw)
and not an inequality (like an unbalanced see-saw), we need to add the same weight (or number) to both
sides.
3. Guided Practice: Work through some simple examples with the class.
A. You have $4.25 to spend at Dave & Buster's. Some games cost $0.75 to play and other games cost $0.50 to
play. You decide to play 2 games that cost $0.75. Write and solve an inequality to find the possible number of
$0.50 games you can play.
B. The school math club has 20 members. Freshmen, sophomores, and juniors may participate in the club. Let
x represent the number of sophomores and let y represent the number of juniors in the club. Write and graph
an inequality that describes the different numbers of sophomores and juniors in the math club.
4. Independent Practice:
A. Brenda bought x number of DVD's at $15 each and received a $10 discount. Simon bought x number of
DVD's for $12.50 each. If they each spent the same amount of money, how many DVD's did Brenda buy?
A. 2 B. 10 C. 4 D. 8
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B. Trader Joe's sells a quart of orange juice for $1.25 and 12 muffins for $5. Michael has a coupon for $0.15 off
each quart of juice if he buys a dozen muffins. How many quarts of orange juice can he buy if he also buys a
dozen muffins without spending more than $10?
A. 4 B. 3 C. 0 D. 10
C. John has $8.25 to spend at a video arcade. Some games cost $0.75 to play and other games cost $0.50 to
play. John decides to play 3 games that cost $0.75. Write and solve an inequality to find the possible number of
$0.50 video games John can play.
D. The JV soccer team has 22 players. Freshmen, sophomores, and juniors may play on the team. Let x
represent the number of sophomores and let y represent the number of juniors on the team. Write and graph
an inequality that describes the different numbers of sophomores and juniors in the math club.
5. Exit Slip
A. What type of operations "undo" each other? Give an example. (Inverse operations: 10 - 7 = 3, 3 + 7 = 10)
B. If you do the same thing to both sides of the = sign, you've ______________ the equation. (balanced)
C. To isolate the variable, get it _____________ on one side of the = sign. (by itself)
D. The __________ of an equation is the answer. (solution)
E. Create your own word problem involving equations in two or more variables to represent relationships
between quantities. Show your work in solving the problem.
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Creating Equations: Solving Two Variable Equations
Name: ____________________ ______ _______
CCSS.Math.Content.HSA.CED.A.2
Date: ______________________ Period: _____
Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
Guided Practice:
A. You have $4.25 to spend at Dave & Buster's. Some games cost $0.75 to play and other games cost $0.50 to
play. You decide to play 2 games that cost $0.75. Write and solve an inequality to find the possible number of
$0.50 games you can play.
B. The school math club has 20 members. Freshmen, sophomores, and juniors may participate in the club. Let
x represent the number of sophomores and let y represent the number of juniors in the club. Write and graph
an inequality that describes the different numbers of sophomores and juniors in the math club.
Independent Practice:
A. Brenda bought x number of DVD's at $15 each and received a $10 discount. Simon bought x number of
DVD's for $12.50 each. If they each spent the same amount of money, how many DVD's did Brenda buy?
A. 2 B. 10 C. 4 D. 8
B. Trader Joe's sells a quart of orange juice for $1.25 and 12 muffins for $5. Michael has a coupon for $0.15 off
each quart of juice if he buys a dozen muffins. How many quarts of orange juice can he buy if he also buys a
dozen muffins without spending more than $10?
A. 4 B. 3 C. 0 D. 10
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All Rights Reserved by NewMathTeacher.Net
C. John has $8.25 to spend at a video arcade. Some games cost $0.75 to play and other games cost $0.50 to
play. John decides to play 3 games that cost $0.75. Write and solve an inequality to find the possible number of
$0.50 video games John can play.
D. The JV soccer team has 22 players. Freshmen, sophomores, and juniors may play on the team. Let x
represent the number of sophomores and let y represent the number of juniors on the team. Write and graph
an inequality that describes the different numbers of sophomores and juniors in the math club.
Exit Slip
A. What type of operations "undo" each other? Give an example. (Inverse operations: 10 - 7 = 3, 3 + 7 = 10)
B. If you do the same thing to both sides of the = sign, you've ______________ the equation. (balanced)
C. To isolate the variable, get it _____________ on one side of the = sign. (by itself)
D. The __________ of an equation is the answer. (solution)
E. Create your own word problem involving equations in two or more variables to represent relationships
between quantities. Show your work in solving the problem.
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Warm-up
Name: ______________________
Simplify the following expressions.
1.
1
3 2 4
2. (2) ∙ 9
3. √
3
Warm-up
Name: ______________________
Simplify the following expressions.
1.
1
3
6 ( 𝑥 + 2) − (−1)
3 2 4
2. (2) ∙ 9
32
3. √ 2 + 3
1
6 (3 𝑥 + 2) − (−1)
3 2 4
2. (2) ∙ 9
32
+
2
Name: ______________________
Simplify the following expressions.
1.
6 (3 𝑥 + 2) − (−1)
3. √
Warm-up
32
+
2
3
Warm-up
Name: ______________________
Simplify the following expressions.
1.
1
3
6 ( 𝑥 + 2) − (−1)
3 2 4
2. (2) ∙ 9
32
3. √ 2 + 3
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net