Question

State which of the following linear equations has solutions (-3, 3), (0, 0), and (3, -3).

a) x+y=0
b) −3x+y=0
c) x+3y=0
d) y=x

Answer 1

The correct linear equation that has solutions (-3, 3), (0, 0), and (3, -3) is a) x + y = 0, as it is the only choice that all three points satisfy.

Step-by-step explanation:

The student is tasked with determining which linear equation from the given options has (-3, 3), (0, 0), and (3, -3) as its solutions. We test each point to see if it satisfies the equation:

• For (-3, 3):
  a) -3 + 3 = 0 (satisfied)
  b) 9 + 3 = 12 (not satisfied)
  c) -3 + 9 = 6 (not satisfied)
  d) 3 = -3 (not satisfied)
• For (0, 0):
  a) 0 + 0 = 0 (satisfied)
  b) 0 + 0 = 0 (satisfied)
  c) 0 + 0 = 0 (satisfied)
  d) 0 = 0 (satisfied)
• For (3, -3):
  a) 3 - 3 = 0 (satisfied)
  b) -9 - 3 = -12 (not satisfied)
  c) 3 - 9 = -6 (not satisfied)
  d) -3 = 3 (not satisfied)

The only equation that is satisfied by all three points is a) x + y = 0. Thus, answer a) x + y = 0 is the correct choice.