Checkpoint: claims, pairs and lines

Which of these satisfies 2x + 3y = 12?

• y = 12 on its own
• x = 6 on its own
• the pair (0, 4)

The first equation of a pair is satisfied by (6, 0). What is known about the second?

• The pair is already solved
• Nothing yet, until (6, 0) is checked there too
• The second equation must also give y = 0

How many pairs satisfy the single equation 2x + 3y = 12?

• Many, one for every point of its line
• Exactly one
• None

Two lines cross between grid marks. What does a careful read-off give?

• An estimate. The exact pair needs algebra
• The exact answer
• Proof that the pair has no solution

A pair is 2x + 3y = 12 with 4x + 6y = 25. What do the lines do?

• Cross once, at a pair with a negative number
• Never meet, because 25 is not double 12
• Lie on top of each other