Question

lines represented by equations 3x-5y=6 and 10y-6x=12 are... *

1 intersecting
2 parallel
3 coincident
4 None of these

​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Lines represented by equations 3x-5y=6 and 10y-6x=12 are

1. Intersecting

2. Parallel

3. Coincident

4. None of these

CONCEPT TO BE IMPLEMENTED

1. General equation of any line in Slope intercept form is

y = mx + c

Where m = Slope of the line

2. Two given straight lines are said to be parallel if they have the same slope

EVALUATION

Here the given equation of the lines are

$\sf{3x - 5y = 6} \: \: \: .......(1)$

$\sf{10y - 6x = 12} \: \: \: ......(2)$

The line given by Equation (1) can be rewritten as below

$\sf{3x - 5y = 6} \: \: \:$

$\implies \sf{5y =3x - 6}$

$\displaystyle \implies \sf{y = \frac{3}{5} x - \frac{6}{5} }$

$\therefore \: \: \displaystyle \sf{Slope \: of \: first \: line = m_1 = \frac{3}{5} }$

The line given by Equation (2) can be rewritten as below

$\sf{10y - 6x = 12} \: \: \:$

$\implies \sf{10y = 6x + 12} \: \: \:$

$\displaystyle \: \implies \sf{y = \frac{3}{5} x + \frac{6}{5} } \: \: \:$

$\therefore \: \: \displaystyle \sf{Slope \: of \: second \: line = m_2 = \frac{3}{5} }$

$\therefore \sf{ \: m_1 = \: m_2}$

Since the given two lines have the same slopes

So the given two lines are parallel

FINAL ANSWER

Lines represented by equations

3x-5y=6 and 10y-6x=12 are

2. Parallel

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