Question

Check whether the lines x+y=1 and 2x +y=x+2 are either parallel or perpendicular
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Answer 1

Given :-

• x + y = 1 .........eq( 1 )

• 2x + y = x + 2

2x - x + y = 2

x + y = 2 ...........eq( 2 )

Solution :-

Let's compare the equations with :-

a1/a2 , b1/b2 , c1/c2

Here,

a1 , a2 , b1 , b2 , c1 , c2 are the coefficient of the given equation.

As we know that,

• a1/a2 ≠ b1/b2 they forms intersecting lines or perpendicular.

• a1/a2 = b1/b2 = c1/c2 they form coincident lines.

• a1 /a2 = b1/b2 ≠ c1/c2 they form parallel lines.

Now, Take equation 1 and

equation 2

a1/a2 = 1/1

b1/b2 = 1/1

c1/ c2 = 1/2

Here, a1/a2 = b1/b2 ≠ c1/c2

Hence, The lines are parallel$.$

Answer 2

Step-by-step explanation:

2x +y -x =2

y = -x +2

y = -x +1

they are parallel not perpendicular....