1

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

A) No

B) Only one solution.

C) Cannot be determined from given information.

D) Yes

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) Yes

B) Cannot be determined from given information.

C) No

D) Only one solution.

5

Which of the following systems of equations has infinite solutions?

A) 3x−y=2
6x−2y=4

B) x−2y=3
3x−6y=9

C) 2x−3y=4
4x−6y=8

D) 4x−2y=6
8x−4y=12

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) 36

B) 9

C) 4

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 = 3 and y can be any value.

C) x can be any value and y = 2.

D) x = 5 and y can be any value.

8

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

A) h = 6

B) h = 5

C) h = 4

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 = 4

D) a = 2, b = 3