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

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(A) Given equations are:$5x - 3y = 11$ (Equation $1$)$-10x + 6y = -22$ (Equation $2$)Comparing with the standard form $a_{1}x + b_{1}y = c_{1}$ and $a

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Consistent

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(A) Given equations are:$5x - 3y = 11$ (Equation $1$)$-10x + 6y = -22$ (Equation $2$)Comparing with the standard form $a_{1}x + b_{1}y = c_{1}$ and $a_{2}x + b_{2}y = c_{2}$:$a_{1} = 5, b_{1} = -3, c_{1} = 11$$a_{2} = -10, b_{2} = 6, c_{2} = -22$Calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{5}{-10} = -\frac{1}{2}$$\frac{b_{1}}{b_{2}} = \frac{-3}{6} = -\frac{1}{2}$$\frac{c_{1}}{c_{2}} = \frac{11}{-22} = -\frac{1}{2}$Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = -\frac{1}{2}$,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.
$5x - 3y = 11$; $-10x + 6y = -22$

Similar Questions

Two lines (coincident) are shown in the following graph. Which option from the following is true for the solution of the pair of linear equations in two variables?

$k$ ની કઈ કિંમત માટે નીચે આપેલ સુરેખ સમીકરણોની જોડને કોઈ ઉકેલ નથી?
$3x + y = 1$
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The graph of the equation ............. passes through the origin.

$A$ line $x-2y=2$ intersects the $Y$-axis at..........

By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them:
$x+y=3$
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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.$5x - 3y = 11$; $-10x + 6y = -22$