a system of equations has no solution. if y = 8x + 7 is one of the equations, which could be the other…

Explanation:

Step1: Recall condition for no - solution

Two linear equations (y = m_1x + b_1) and (y=m_2x + b_2) have no solution when (m_1=m_2) and (b_1\neq b_2) (parallel lines). The given equation is (y = 8x+7), so (m_1 = 8) and (b_1=7).

Step2: Rewrite each option in slope - intercept form (y=mx + b)

Option 1:

Starting with (2y = 16x + 14), divide by 2: (y=\frac{16x + 14}{2}=8x + 7). Here (m = 8) and (b = 7), same as the given line (coincident lines, infinite solutions).

Option 2:

The equation (y = 8x-7) has (m = 8) and (b=-7). Since (m = 8) (same as the given line) and (b=-7\neq7), these are parallel lines and the system has no solution.

Option 3:

The equation (y=-8x + 7) has (m=-8\neq8), so the lines are not parallel.

Option 4:

Starting with (2y=-16x - 14), divide by 2: (y=\frac{-16x - 14}{2}=-8x-7), (m=-8\neq8), so the lines are not parallel.

Answer:

(y = 8x-7)