Question

Match the graph with the correct set of equations for the linear system. Then, classify the system as Consistent and Dependent, Consistent and Independent, or Inconsistent. (You should have two answers selected)

Answer 1

Consistent independent

x + y = 0 and -x + y = -8

Explanation:

Inconsistent: parallel lines, no solutions

Consistent dependent: same line, infinite solutions

Consistent independent: intersects at one point, one solution

Therefore, the pair of lines are Consistent independent

From inspection of the diagram:

One line has a negative slope and the other a positive slope.

One has a y-intercept of 0 and the other a y-intercept of -8.

Therefore, the solution is x + y = 0 and -x + y = -8

Because:

x + y = 0 ⇒ y = -x (neg slope, y-intercept of 0)

-x + y = -8 ⇒ y = x - 8 (pos slope, y-interecept at -8)