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

a system of equations has no solution. if y = 8x + 7 is one of the equations, which could be the other equation? 2y = 16x + 14 y = 8x - 7 y = -8x + 7 2y = -16x - 14

Answer

Explanation:

Step1: Recall the condition for no - solution

A system of linear equations (y = m_1x + b_1) and (y=m_2x + b_2) has no solution when (m_1=m_2) and (b_1\neq b_2). The given equation is (y = 8x+7), so (m_1 = 8) and (b_1 = 7).

Step2: Analyze each option

For (2y=16x + 14), rewrite it in slope - intercept form (y = 8x+7). Here (m = 8) and (b = 7), the system has infinitely many solutions.
For (y = 8x-7), (m = 8) and (b=-7). Since (m_1 = m_2=8) and (b_1 = 7\neq b_2=-7), this equation will make the system have no solution.
For (y=-8x + 7), (m=-8\neq8), the system has a unique solution.
For (2y=-16x-14), rewrite it as (y=-8x - 7), (m=-8\neq8), the system has a unique solution.

Answer:

(y = 8x-7)