SaiBook.us SAT-2

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: System of Linear Equations with Infinite Solutions

Grade: 1300-a Lesson: S1-L7

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: in Class

Problem Id	Problem	Options
1	Consider the system of equations: 2x + 3y = 7 4x + 6y = 14 Does this system have infinite solutions?	A) Yes B) Only one solution C) Cannot be determined from given information D) No
2	Which of the following systems of equations has infinite solutions?	A) 3x - y = 4 6x - 2y = 8 B) x + 2y = 5 2x + 4y = 10 C) 2x + 3y = 6 4x + 6y = 12 D) 2x + 5y = 10 4x + 10y = 20
3	For which values of K does the system of equations have infinite solutions? 2x + 3y = 5 4x + Ky = 10	A) K = 9 B) K = 6 C) K = 4 D) K = 2
4	Determine if the system of equations has infinite solutions: 3x - y = 2 6x - 2y = 4	A) Only one solution B) Cannot be determined from given information C) No D) Yes
5	Which of the following systems of equations has infinite solutions?	A) 3x - y = 2 6x - 2y = 4 B) 4x - 2y = 6 8x - 4y = 12 C) 2x - 3y = 4 4x - 6y = 8 D) x - 2y = 3 3x - 6y = 9
6	2x + 7y = 9 8x + 28y = a In the given system of equations, a is a constant. If the system has infinitely many solutions, what is the value of a?	A) 4 B) 9 C) 36 D) 54
7	A park charges $x for entry and $y per hour for parking. A family decides to either pay for parking and walk around the park or skip parking and take a free shuttle that circles the park. They end up paying a total of $5 for either option. Write down a system of equations representing this situation and find the values of x and y for which there are infinitely many solutions.	A) x can be any value and y = 5 B) x = 5 and y can be any value x C) can be any value and y = 2 D) x = 3 and y can be any value 6
8	Find all values of h for which the following system has infinitely many solutions: x + 2y = 3 2x + hy = h + 3	A) h = 4 B) h = 5 C) h = 6 D) h = 7
9	Find the values of k for which the following system of linear equations has infinite solutions: x + 2y − z = 3 2x + 4y − 2z = 6 kx + 6y − 3z = 9	A) k = 2 B) k = 3 C) k = 4 D) k = 5
10	Determine the values of a and b such that the system below has infinitely many solutions: 2x + 3y = 5 ax + by = 5	A) a = 2, b = 1 B) a = 2, b = 2 C) a = 2, b = 3 D) a = 2, b = 4

Problem Id

Problem

Options

Consider the system of equations:
2x + 3y = 7
4x + 6y = 14
Does this system have infinite solutions?

A) Yes

B) Only one solution

C) Cannot be determined from given information

D) No

Which of the following systems of equations has infinite solutions?

A) 3x - y = 4
6x - 2y = 8

B) x + 2y = 5
2x + 4y = 10

C) 2x + 3y = 6
4x + 6y = 12

D) 2x + 5y = 10
4x + 10y = 20

For which values of K does the system of equations have infinite solutions?
2x + 3y = 5
4x + Ky = 10

A) K = 9

B) K = 6

C) K = 4

D) K = 2

Determine if the system of equations has infinite solutions:
3x - y = 2
6x - 2y = 4

A) Only one solution

B) Cannot be determined from given information

C) No

D) Yes

Which of the following systems of equations has infinite solutions?

A) 3x - y = 2
6x - 2y = 4

B) 4x - 2y = 6
8x - 4y = 12

C) 2x - 3y = 4
4x - 6y = 8

D) x - 2y = 3
3x - 6y = 9

2x + 7y = 9
8x + 28y = a
In the given system of equations, a is a constant. If the system has infinitely many solutions, what is the value of a?

A) 4

B) 9

C) 36

D) 54

A park charges $x for entry and $y per hour for parking. A family decides to either pay for parking and walk around the park or skip parking and take a free shuttle that circles the park. They end up paying a total of $5 for either option. Write down a system of equations representing this situation and find the values of x and y for which there are infinitely many solutions.

A) x can be any value and y = 5

B) x = 5 and y can be any value x

C) can be any value and y = 2

D) x = 3 and y can be any value 6

Find all values of h for which the following system has infinitely many solutions:
x + 2y = 3
2x + hy = h + 3

A) h = 4

B) h = 5

C) h = 6

D) h = 7

Find the values of k for which the following system of linear equations has infinite solutions:
x + 2y − z = 3
2x + 4y − 2z = 6
kx + 6y − 3z = 9

A) k = 2

B) k = 3

C) k = 4

D) k = 5

Determine the values of a and b such that the system below has infinitely many solutions:
2x + 3y = 5
ax + by = 5

A) a = 2, b = 1

B) a = 2, b = 2

C) a = 2, b = 3

D) a = 2, b = 4