What is the intersection point for equations x-3=0 and y-5=0?

a) 5,3
b) 3,5
c) 0,-5
d) None of these

Question by Mohit

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According to the question,

x-3=0 and y-5=0
But, we know that we need two variables for forming a line on the graph. But here we got only x as the variable in first equation and y as the variable in the second equation. But here y is formed as 0y in first equation and x is formed as 0x in the second equation. But in the question they are shown as they are not present.
Now they equations became,
x+0y-3=0 and 0x+y-5=0
Now if we take x=3 and y=0;
$\Rightarrow$ 3+0-3=0
$\Rightarrow$ 0=0
$\therefore$ x=3 and y=0 satisfy the equation.

Now if we take x=3 and y=5;
$\Rightarrow$ 3+(0)(5)-3=0
$\Rightarrow$ 3+0-3=0
$\Rightarrow$ 3-3=0
$\Rightarrow$ 0=0
$\therefore$ x=3 and y=5 satisfy the equation.

Now for the equation 0x+y-5=0,
Now if we take x=0 and y=5,
$\Rightarrow$ 0+5-5=0
$\Rightarrow$ 0=0
$\therefore$ x=0 and y=5 satisfy this equation

Now if we take x=3 and y=5,
$\Rightarrow$ (0)(3)+5-5=0
$\Rightarrow$ 0+5-5=0
$\Rightarrow$ 0=0
$\therefore$ x=3 and y=5 satisfy the equation.

The both equations have point (3,5) as common so they would intersect at (3,5).
So, option B is correct.

The graph will look like this:

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