Question

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

Explanation:

Step1: Recall no-solution condition

A linear system

$$\begin{cases}y=m_1x+b_1\\y=m_2x+b_2\end{cases}$$

has no solution if $m_1=m_2$ and $b_1
eq b_2$ (parallel, non-coinciding lines).

Step2: Analyze each option

Option1: Simplify $2y=1.6x+14$

Divide by 2: $y=0.8x+7$. Here $m=0.8
eq8$, so not parallel.

Option2: Check $y=8x-7$

Here $m=8$ (matches $y=8x+7$) and $b=-7
eq7$. Satisfies no-solution condition.

Option3: Check $y=-8x+7$

Here $m=-8
eq8$, so not parallel.

Option4: Simplify $2y=-16x-14$

Divide by 2: $y=-8x-7$. Here $m=-8
eq8$, so not parallel.

Answer:

$\boldsymbol{y = 8x - 7}$