the lines 2(x-y) = 3, 6x +5 = 6y are parellel, state true or false

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Solution

$The given system of equations is : 2 (x - y) = 3 \Rightarrow 2 x - 2 y - 3 = 0 . . . (1) 6 x - 6 y + 5 = 0 . . . . (2) Comparing the above equations with a_{1} x + b_{1} y + c_{1} = 0 and a_{2} x + b_{2} y + c_{2} = 0, we get a_{1} = 2; b_{1} = - 2; c_{1} = - 3 a_{2} = 6; b_{2} = - 6; c_{2} = 5 Now, \frac{a_{1}}{a_{2}} = \frac{2}{6} = \frac{1}{3} \frac{b_{1}}{b_{2}} = \frac{- 2}{- 6} = \frac{1}{3} \frac{c_{1}}{c_{2}} = - \frac{3}{5} Since, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} Hence, the lines represented by given equations are parallel to each other .$

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