Math, asked by ramya4611, 1 month ago

The two lines 2x + 3y = 7, 8x + 12y = 1 are________lines
A)
Perpendicular
B)
Parallel
c) Intersecting
D)
coincident​

Answers

Answered by deepjaiswal522
2

Answer:

coincident it right or wrong

please you can tell me the answer

Answered by pulakmath007
0

The two lines 2x + 3y = 7 , 8x + 12y = 1 are parallel lines [ The correct option is B) Parallel ]

Given :

The lines 2x + 3y = 7 , 8x + 12y = 1

To find :

The two lines 2x + 3y = 7 , 8x + 12y = 1 are________lines

A) Perpendicular

B) Parallel

C) Intersecting

D) Coincident

Concept :

For the given two lines

\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}

1. Intersecting lines :

\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }

2. Coincident lines :

\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}

3. Parallel lines :

\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}

4. Perpendicular lines :

\displaystyle \sf{ \: {a_1}{a_2} + {b_1}{b_2}=0 }

Solution :

Step 1 of 2 :

Write down the given pair of equations

Here the given pair of linear equations are

2x + 3y = 7 - - - - - (1)

8x + 12y = 1 - - - - - (2)

Step 2 of 2 :

Specifiy the name of the lines

The given pair of lines can be rewritten as

2x + 3y - 7 = 0 - - - - - (1)

8x + 12y - 1 = 0 - - - - - (2)

Comparing with the equations

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 we get

a₁ = 2 , b₁ = 3 , c₁ = - 7 and a₂ = 8 , b₂ = 12 , c₂ = - 1

Now we have ,

\displaystyle \sf\frac{a_1}{a_2} = \frac{2}{8}   =  \frac{1}{4}

\displaystyle \sf \frac{b_1}{b_2} =  \frac{3}{12}   =  \frac{1}{4}

\displaystyle \sf \frac{c_1}{c_2} = \frac{ - 7}{ - 1} =7

\displaystyle \sf \therefore \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}

∴ The two lines 2x + 3y = 7 , 8x + 12y = 1 are parallel lines

Hence the correct option is B) Parallel

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Learn more from Brainly :-

1. how many solution does the pair of equations 3x + 4y + 2 = 0 , 4x = 5y - 13 have ? give reason

https://brainly.in/question/4061875

2. the pair of equations 3x-5y=7 and -6x+10y=7 has

https://brainly.in/question/17643487

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