Question

find whether the lines represented by 2x+y = 3 and 4x+2y = 6 are parallel, consistent or intersecting.​

Answer 1

Step-by-step explanation:

The given line are parallel.

Step-by-step explanation:

Given : The lines represented by 2x+y=3 and 4x+2y=6 are parallel, coincident or intersecting.

To find : Whether the lines are parallel?

Solution :

According to the lines,

a_1=2 ,b_1=1 ,c_1=-3a

1

=2,b

1

=1,c

1

=−3

a_2=4,b_2=2 ,c_2=-6a

2

=4,b

2

=2,c

2

=−6

When the lines are parallel, coincident or intersecting,

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

a

2

a

1

=

b

2

b

1

=

c

2

c

1

\frac{2}{4}=\frac{1}{2}=\frac{-3}{-6}

4

2

=

2

1

=

−6

−3

\frac{1}{2}=\frac{1}{2}=\frac{1}{2}

2

1

=

2

1

=

2

1

Condition satisfied by the points.

Therefore, The given line are parallel.