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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: System of Linear Equations with no Solutions

Grade: 1300-a Lesson: S1-L8

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	A store sells only apples and oranges. The total number of fruits sold is 20, and the total revenue is $30. Apples sell for $1 each and oranges sell for $2 each. How many apples and oranges were sold?	A) 8 apples and 11 oranges B) 9 apples and 10 oranges C) 10 apples and 10 oranges D) 11 apples and 10 oranges
2	If there is no solution to the linear equation system \$ (20 \times 2)"m"\$ = 36 - dn, 20m = 16 + 4n, then find the value of d + 12.	A) 1 B) 2 C) 3 D) 4
3	The temperature in a city at noon is 20°C. From noon to midnight, the temperature decreases by 10°C. At midnight, the temperature is 5°C. Determine the rate of temperature change per hour.	A) 1.5°C/hour B) 1.25°C/hour C) 1.0°C/hour D) 0.75°C/hour
4	You are given a system of two linear equations in two variables (x and y). Which of the following statements ALWAYS guarantees there are NO solutions?	A) Both equations have the same slope but different y-intercepts. B) Both equations have the same slope but different y-intercepts. C) Both equations have different slopes but the same x-intercept. D) The coefficients of one variable in both equations are zero (e.g., x terms are missing in both).
5	Solve the following system of equations and determine the number of solutions: 2x + 3y = 6 4x + 6y = 10	A) No solution B) Infinitely many solutions C) Unique solution D) None of these above
6	A school math club consists of boys and girls. There are 20 students in total, and the ratio of boys to girls is 3:2. However, due to an error in counting, it was mistakenly reported that the ratio of boys to girls was 4:3. Determine how many boys and girls are in the math club.	A) 11 boys and 8 girls B) 12 boys and 8 girls C) 13 boys and 10 girls D) 14 boys and 9 girls
7	Find the value of p and q : - 5p - 10q = 20 and p + 30 = \$ - (6 \times (4q)) \$.	A) \$ p = 15/13, q = −19/13 \$ B) \$ p = 18/13, q = −17/13 \$ C) \$ p = 19/13, q = −17/13 \$ D) \$ p = 18/13, q = −15/13 \$
8	Emma has a collection of quarters and dimes. The total number of coins is 6, and their total value is $1.20. How many quarters and how many dimes does she have?	A) 2 quarters and 3 dimes B) 6 quarters and 2 dimes C) 4 quarters and 2 dimes D) 5 quarters and 2 dimes
9	A mixture of sugar and flour contains 20% sugar. Another mixture contains 30% sugar. How much of each mixture should be combined to create 100 kg of a mixture that is 25% sugar?	A) 40 kg of the 20% sugar mixture and 60 kg of the 30% sugar mixture. B) 70 kg of the 20% sugar mixture and 30 kg of the 30% sugar mixture. C) 50 kg of the 20% sugar mixture and 50 kg of the 30% sugar mixture. D) 60 kg of the 20% sugar mixture and 40 kg of the 30% sugar mixture.
10	Find the value of r: 7r + 3s = 16 and 4r − s = −15	A) \$ -17/19 \$ B) \$ -21/19 \$ C) \$ -9/19 \$ D) \$ -29/19 \$

Problem Id

Problem

Options

A store sells only apples and oranges. The total number of fruits sold is 20, and the total revenue is $30.
Apples sell for $1 each and oranges sell for $2 each. How many apples and oranges were sold?

A) 8 apples and 11 oranges

B) 9 apples and 10 oranges

C) 10 apples and 10 oranges

D) 11 apples and 10 oranges

If there is no solution to the linear equation system
\$ (20 \times 2)"m"\$ = 36 - dn, 20m = 16 + 4n, then find the value of d + 12.

A) 1

B) 2

C) 3

D) 4

The temperature in a city at noon is 20°C. From noon to midnight, the temperature decreases by 10°C. At midnight, the temperature is 5°C. Determine the rate of temperature change per hour.

A) 1.5°C/hour

B) 1.25°C/hour

C) 1.0°C/hour

D) 0.75°C/hour

You are given a system of two linear equations in two variables (x and y). Which of the following statements ALWAYS guarantees there are NO solutions?

A) Both equations have the same slope but different y-intercepts.

B) Both equations have the same slope but different y-intercepts.

C) Both equations have different slopes but the same x-intercept.

D) The coefficients of one variable in both equations are zero (e.g., x terms are missing in both).

Solve the following system of equations and determine the number of solutions:
2x + 3y = 6
4x + 6y = 10

A) No solution

B) Infinitely many solutions

C) Unique solution

D) None of these above

A school math club consists of boys and girls. There are 20 students in total, and the ratio of boys to girls is 3:2. However, due to an error in counting, it was mistakenly reported that the ratio of boys to girls was 4:3. Determine how many boys and girls are in the math club.

A) 11 boys and 8 girls

B) 12 boys and 8 girls

C) 13 boys and 10 girls

D) 14 boys and 9 girls

Find the value of p and q :
- 5p - 10q = 20 and p + 30 = \$ - (6 \times (4q)) \$.

A) \$ p = 15/13, q = −19/13 \$

B) \$ p = 18/13, q = −17/13 \$

C) \$ p = 19/13, q = −17/13 \$

D) \$ p = 18/13, q = −15/13 \$

Emma has a collection of quarters and dimes. The total number of coins is 6, and their total value is $1.20. How many quarters and how many dimes does she have?

A) 2 quarters and 3 dimes

B) 6 quarters and 2 dimes

C) 4 quarters and 2 dimes

D) 5 quarters and 2 dimes

A mixture of sugar and flour contains 20% sugar. Another mixture contains 30% sugar. How much of each mixture should be combined to create 100 kg of a mixture that is 25% sugar?

A) 40 kg of the 20% sugar mixture and 60 kg of the 30% sugar mixture.

B) 70 kg of the 20% sugar mixture and 30 kg of the 30% sugar mixture.

C) 50 kg of the 20% sugar mixture and 50 kg of the 30% sugar mixture.

D) 60 kg of the 20% sugar mixture and 40 kg of the 30% sugar mixture.

Find the value of r:
7r + 3s = 16 and 4r − s = −15

A) \$ -17/19 \$

B) \$ -21/19 \$

C) \$ -9/19 \$

D) \$ -29/19 \$