Question

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

Answer 1

Answer:

2x+3y=7 and 8x+12y=1

a1/a2 = b1/b2 is not equal to c1/c2

2/8 = 3/12 is not equal to 1/7

1/8 = 1/4 is not equal to 1/7

so the equation are parallel lines

Answer 2

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

Correct question : The two lines 2x + 3y = 7 , 8x + 12y = 1 are________lines. A) Perpendicular B) Parallel C) Intersecting D) Coincident

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 - - - - - (3)

8x + 12y - 1 = 0 - - - - - (4)

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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