The pair of equations $y =0$ and$y =-7$has:

 

 

Given that,

The pair of equations $𝑦 = 0$ and $𝑦 =- 7$ 

The linear equation of $𝑦 = 0$ is, 0. $𝑥 + 1$. $𝑦 + 0 = 0$ 

Here,$𝑎₁ = 0, 𝑏₁=1, c₁=0$

The linear equation of$𝑦 =- 7$ is, 0. $𝑥 + 1$. $𝑦 - 7 = 0$

Here, $a₂=0, b₂=1, c₂=7$

$\frac{𝑎₁}{𝑎₂}=\frac{0}{0}=1, \frac{𝑏₁}{𝑏₂}=\frac{1}{1},\frac{𝑐₁ }{𝑐₂}=\frac{0}{7}$

$\frac{𝑎₁}{𝑎₂}= \frac{𝑏₁}{𝑏₂}\ne \frac{𝑐₁ }{𝑐₂}$

The two lines are parallel. 

Hence they do not intersect at any point

So, the pair of equations 𝑦 = 0 and 𝑦 =− 7 has no solutions. Hence option (𝑑) no solutions is correct.