Question

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

Explanation:

Step1: Recall no-solution condition

A system of linear equations $y = m_1x + b_1$ and $y = m_2x + b_2$ has no solution if $m_1 = m_2$ (same slope) and $b_1
eq b_2$ (different y-intercepts).

Step2: Analyze given equation

The given equation is $y = 8x + 7$, where slope $m_1 = 8$ and y-intercept $b_1 = 7$.

Step3: Simplify each option

• Option1: $2y = 16x + 14$ simplifies to $y = 8x + 7$. Here $m_2=8$, $b_2=7$ (same as given, infinite solutions).
• Option2: $y = 8x - 7$. Here $m_2=8$, $b_2=-7$ (same slope, different intercept).
• Option3: $y = -8x + 7$. Here $m_2=-8

eq 8$ (different slope, one solution).

• Option4: $2y = -16x -14$ simplifies to $y = -8x -7$. Here $m_2=-8

eq 8$ (different slope, one solution).

Answer:

B. $y = 8x - 7$