Is the pair of equations x+2y-3=0 and 6y+3x-9 | vedclass

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(A) Given equations are $x+2y-3=0$ and $3x+6y-9=0$.Comparing these with the standard form $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$,we get:$a_1=1, b_1=2

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Yes,they are consistent.

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(A) Given equations are $x+2y-3=0$ and $3x+6y-9=0$.Comparing these with the standard form $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$,we get:$a_1=1, b_1=2, c_1=-3$$a_2=3, b_2=6, c_2=-9$Now,calculating the ratios:$\frac{a_1}{a_2} = \frac{1}{3}$$\frac{b_1}{b_2} = \frac{2}{6} = \frac{1}{3}$$\frac{c_1}{c_2} = \frac{-3}{-9} = \frac{1}{3}$Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,the lines are coincident.Therefore,the pair of equations has infinitely many solutions and is consistent.

Is the pair of equations $x+2y-3=0$ and $6y+3x-9=0$ consistent? Justify your answer.

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