Solving pairs of linear equations in two variables

The pair of equations y = 0 and y = -7 has

• One solution

• Two solutions

• Infinitely many solutions

• No solution

Arjun and Charlotte are trying to solve a problem. They have two equations representing the number of apples (x) and oranges (y) they have:

2x + y = -12

-4x -2y = 30

Can you help them find a solution?

If two lines have the exact same slope but different y-intercepts, those two lines will

• sometimes  have no solution
• always have no solution
• sometimes have one solution
• always have one solution

2x + 4y = 0

-5x - 4y = 18

• (6, -6)

• (-6, 3)

• Infinite solutions

• No solutions

Elijah, David, and Daniel are trying to meet up, but they can't seem to find a common location. If they each represent a line in a system of equations, what does it mean if they can't find a common meeting point?

• They are all heading to the same location

• They are all heading in different directions without any intersection

• They will all meet at one specific location

• They are all heading in directions that are perpendicular to each other

The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have any solutions if : 

• k = 5
• k = 10
• k ≠ 10
• k ≠ 5

which is correct statement for inconsistent equations

• they have only unique solution

• they have only infinite solutions

• they have no solution

• they may have unique or infinite solutions

When solving a system of equations algebraically, which statement results in no solution?

• 4 = 7

• 2 = 2

• x = 5, y = 2

• (0, 0)

T-Rob is solving the system shown. What is the solution?

• (-1, 3)

• (3, -1)

• There is no solution.

• There are infinitely many solutions.

While solving a system algebraically, Jenna creates the equation 0 = 4.  How many solutions does the system have?

• one
• none
• infinitely many