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

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(A) Given equations are:$1) \frac{3}{2} x + \frac{5}{3} y = 7 \implies \frac{3}{2} x + \frac{5}{3} y - 7 = 0$$2) 9 x - 10 y = 14 \implies 9 x - 10 y -

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Consistent

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(A) Given equations are:$1) \frac{3}{2} x + \frac{5}{3} y = 7 \implies \frac{3}{2} x + \frac{5}{3} y - 7 = 0$$2) 9 x - 10 y = 14 \implies 9 x - 10 y - 14 = 0$Comparing with $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$:$a_{1} = \frac{3}{2}, b_{1} = \frac{5}{3}, c_{1} = -7$$a_{2} = 9, b_{2} = -10, c_{2} = -14$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{3/2}{9} = \frac{3}{18} = \frac{1}{6}$$\frac{b_{1}}{b_{2}} = \frac{5/3}{-10} = \frac{5}{-30} = -\frac{1}{6}$Since $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2}}$,the lines intersect at a unique point.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.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

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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.$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

Similar Questions

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Solve the following pair of linear equations by the elimination method and the substitution method:$\frac{x}{2} + \frac{2y}{3} = -1$ and $x - \frac{y}{3} = 3$

Solve the following pair of equations by reducing them to a pair of linear equations:$\frac{1}{2x} + \frac{1}{3y} = 2$$\frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$

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Solve the following pair of linear equations by the substitution and cross-multiplication methods:$8x + 5y = 9$$3x + 2y = 4$