Question

The pair of equations $x=a$ and $y=b$ graphically represents lines which are

• A. parallel
• B. intersecting at $(b,a)$
• C. coincident
• D. intersecting at $(a,b)$

Answer 1

Answer: (D)

intersecting at $(a,b)$

The equations are $x=a$ and $y=b$.

The graph of $x=a$ is a line parallel to $y$-axis and $y=b$ is a line parallel to $x$-axis.

$\therefore$ the angle between them is ${90}^o$, i.e. they intersect.

So, the equations are consistent.

Now solving simultaneously, the solution is $(a,b)$.

So, the point of intersection is $(a,b)$.

Hence, option D is correct.