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

Inconsistent

4x + 2y = 6 and 4y = -8x + 4

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 INCONSISTENT.

Both lines have negative slopes. As they are parallel, the slopes will be the same for both lines.

Therefore, solution is:

4x + 2y = 6 and 4y = -8x + 4

Because:

4x + 2y = 6 ⇒ y = -2x + 3

4y = -8x + 4 ⇒ y = -2x + 1

Both lines have same slope of -2