On comparing the ratios frac{a_{1}}{a_{2}}, f | vedclass

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(A) Given equations are:$1) \frac{4}{3} x + 2 y - 8 = 0$$2) 2 x + 3 y - 12 = 0$Comparing with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{

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(A) Given equations are:$1) \frac{4}{3} x + 2 y - 8 = 0$$2) 2 x + 3 y - 12 = 0$Comparing with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$a_{1} = \frac{4}{3}, b_{1} = 2, c_{1} = -8$$a_{2} = 2, b_{2} = 3, c_{2} = -12$Calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{4/3}{2} = \frac{4}{6} = \frac{2}{3}$$\frac{b_{1}}{b_{2}} = \frac{2}{3}$$\frac{c_{1}}{c_{2}} = \frac{-8}{-12} = \frac{2}{3}$Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$,the lines are coincident.Because the lines are coincident,they have infinitely many solutions.Therefore,the pair of linear equations is consistent.

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

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On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$