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)

Please answer and explain.

Answer 1

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Answer 2

Answer:

Option D is correct

Step-by-step explanation:

Given Equations are

x = a   and y = b

in standard form   x + 0.y - a =0    and 0.x + y -b = 0

By comparing with standard form of equation,

$a_1x+b_1y+c_1=0\:\:and\:\:a_2x+b_2y+c_2=0$

Ratios we get are

$\frac{a_1}{a_2}=\frac{1}{0}\:\:,\:\:\frac{b_1}{b_2}=\frac{0}{1}\:\:and\:\:\frac{c_1}{c_2}=\frac{-a}{-b}=\frac{a}{b}$

Since, $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$

Given lines are intersecting lines.

Point of intersection is x = a & y = b .i.e., ( a , b )

Therefore, Option D is correct