Question

the graphs of the equation x-y=-2 and 2x-2y=-4 appears​

Answer 1

Answer:

The graphs of the equations appears on the same line because both are coincident.

Note:

★ If we considered two equations of line ; ax + by + c = 0 and a'x + b'y + c' =0 .

Then ;

• If a/a' = b/b' = c/c' , then both the lines are coincidence.

• If a/a' = b/b' ≠ c/c' , then both the lines are coincident.

• If a/a' ≠ b/b' , then both the lines intersect each other at a distinct point.

Solution:

The given equations of lines are :

x - y = -2 ---------(1)

2x - 2y = -4 ---------(2)

Eq-(1) can be rewritten as ;

x - y + 2 = 0 -------(3)

Eq-(2) can be rewritten as ;

2x - 2y + 4 = 0 ------(4)

Observing eq-(3) and (4) , we get ;

a = 1

a' = 2

b = -1

b' = -2

c = 2

c' = 4

Now,

a/a' = 1/2

b/b' = -1/-2 = 1/2

c/c' = 2/4 = 1/2

Clearly,

a/a' = b/b' = c/c'

Hence,

Both the lines are coincident , hence the graphs of both the equations overlap each other .

Thus,

Graphs of both the equations appears on same line .