Find whether the lines representing the following pair of linear equation intersect at a point, are parallel or coincident . $\frac{3 x}{2} - \frac{5 y}{3} = - 2; \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

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Solution

$\frac{3 x}{2} - \frac{5 y}{3} + 2 = 0$

$m = \frac{- \frac{3}{2}}{- \frac{5}{3}} = + \frac{9}{10}$

$\frac{x}{3} + \frac{y}{2} - \frac{13}{6} = 0$

$m = \frac{- \frac{1}{3}}{\frac{1}{2}} = - \frac{2}{3}$

Slopes are not the same, therefore lines are parallel neither coincident, they intersect.

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Find whether the lines representing the following pair of linear equation intersect at a point, are parallel or coincident . 3x2−5y3=−2;x3+y2=136

3x2−5y3+2=0m=−32−53=+910x3+y2−136=0m=−1312=−23Slopes are not the same, therefore lines are parallel neither coincident, they intersect.

Find whether the lines representing the following pair of linear equation intersect at a point, are parallel or coincident . $\frac{3 x}{2} - \frac{5 y}{3} = - 2; \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

$\frac{3 x}{2} - \frac{5 y}{3} + 2 = 0$

$m = \frac{- \frac{3}{2}}{- \frac{5}{3}} = + \frac{9}{10}$

$\frac{x}{3} + \frac{y}{2} - \frac{13}{6} = 0$

$m = \frac{- \frac{1}{3}}{\frac{1}{2}} = - \frac{2}{3}$

Slopes are not the same, therefore lines are parallel neither coincident, they intersect.