Problem Overview:
The task involves solving algebraic expressions with two variables and using the solutions to color a picture according to a provided code. The goal is to evaluate each expression for the given values of \( x \) and \( y \), determine if the statement is true or false, and then use the corresponding color from the answer key to fill in the sections of the image.
Step-by-Step Solution:
####
Given Values:
- \( x = 5 \)
- \( y = 3 \)
####
Expressions to Evaluate:
1.
Expression 1: \( 7 + x > 10 \)
- Substitute \( x = 5 \):
\[
7 + 5 > 10 \implies 12 > 10
\]
- This is
true.
- According to the answer key,
true corresponds to
Light Blue.
2.
Expression 2: \( x + y > 12 \)
- Substitute \( x = 5 \) and \( y = 3 \):
\[
5 + 3 > 12 \implies 8 > 12
\]
- This is
false.
- According to the answer key,
false corresponds to
Orange.
3.
Expression 3: \( x + 2y = 11 \)
- Substitute \( x = 5 \) and \( y = 3 \):
\[
5 + 2(3) = 11 \implies 5 + 6 = 11 \implies 11 = 11
\]
- This is
true.
- According to the answer key,
true corresponds to
Light Blue.
4.
Expression 4: \( 2x + y < 9 \)
- Substitute \( x = 5 \) and \( y = 3 \):
\[
2(5) + 3 < 9 \implies 10 + 3 < 9 \implies 13 < 9
\]
- This is
false.
- According to the answer key,
false corresponds to
Orange.
5.
Expression 5: \( x + y > 7 \)
- Substitute \( x = 5 \) and \( y = 3 \):
\[
5 + 3 > 7 \implies 8 > 7
\]
- This is
true.
- According to the answer key,
true corresponds to
Light Blue.
6.
Expression 6: \( 3x + y = 18 \)
- Substitute \( x = 5 \) and \( y = 3 \):
\[
3(5) + 3 = 18 \implies 15 + 3 = 18 \implies 18 = 18
\]
- This is
true.
- According to the answer key,
true corresponds to
Light Blue.
7.
Expression 7: \( x + 2y = 11 \)
- This is the same as Expression 3, so it is
true.
- According to the answer key,
true corresponds to
Light Blue.
8.
Expression 8: \( 2x + y < 9 \)
- This is the same as Expression 4, so it is
false.
- According to the answer key,
false corresponds to
Orange.
9.
Expression 9: \( x + y > 7 \)
- This is the same as Expression 5, so it is
true.
- According to the answer key,
true corresponds to
Light Blue.
10.
Expression 10: \( 3x + y = 18 \)
- This is the same as Expression 6, so it is
true.
- According to the answer key,
true corresponds to
Light Blue.
####
Summary of Results:
- True statements: Light Blue
- Expressions: 1, 3, 5, 6, 7, 9, 10
- False statements: Orange
- Expressions: 2, 4, 8
Final Answer:
\[
\boxed{\text{See the solution above for the coloring instructions.}}
\]
Using the results, you can now color the corresponding sections of the image based on the truth value of each expression. True statements are colored
Light Blue, and false statements are colored
Orange.
Parent Tip: Review the logic above to help your child master the concept of algebra coloring worksheet.
