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Two lines are given to be …

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Two lines are given to be parallel. The equation of one of the line is 4x+3y=14, then find the equation of second line.
  • 1 answers

Sia ? 6 years, 6 months ago

Equation of a line ax + by + c = 0 parallel to given line is ax + by + k = 0, here k is any real number.
The equation of one line is 4x + 3y = 14.
a1 = 4 , b1 = 3 and c1=  - 14
Two lines are given to be parallel. So, No solutions and the pair of linear equations is inconsistent.

{tex}\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c _ { 2 } }{/tex}
or
{tex}\frac{4}{{{a_2}}} = \frac{3}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}} {/tex}
{tex}\Rightarrow \frac{{{a_2}}}{{{b_2}}} = \frac{4}{3} = \frac{{12}}{9}{/tex}

Hence, one of the possible, second parallel line is 12x + 9y = 5.

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