5. The pair of equations \(x = a\) and \(y = b\) graphically represents lines which are
parallel
intersecting at (b, a)
coincident
intersecting at (a, b)
Step 1: Understand the equations.
The equation \(x = a\) is a vertical line passing through all points where the \(x\)-coordinate is always \(a\).
The equation \(y = b\) is a horizontal line passing through all points where the \(y\)-coordinate is always \(b\).
Step 2: Check their intersection.
The vertical line \(x = a\) and the horizontal line \(y = b\) meet at a single point.
This point has coordinates where \(x = a\) and \(y = b\), i.e., the point \((a, b)\).
Step 3: Verify the options.
(A) Parallel → Incorrect, since they cross each other.
(B) Intersecting at \((b,a)\) → Incorrect, order of coordinates is wrong.
(C) Coincident → Incorrect, because the lines are distinct and not overlapping.
(D) Intersecting at \((a,b)\) → Correct, since that is the only common point.
Final Answer: Option (D), the lines intersect at \((a,b)\).