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(A) To check if the pair of equations is consistent,we compare the ratios of the coefficients: $a_1 = 2, b_1 = 4, c_1 = -9$ $a_2 = 3, b_2 = 6, c_2 = -

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Consistent

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(A) To check if the pair of equations is consistent,we compare the ratios of the coefficients: $a_1 = 2, b_1 = 4, c_1 = -9$ $a_2 = 3, b_2 = 6, c_2 = -\frac{27}{2}$ Calculating the ratios: $\frac{a_1}{a_2} = \frac{2}{3}$ $\frac{b_1}{b_2} = \frac{4}{6} = \frac{2}{3}$ $\frac{c_1}{c_2} = \frac{-9}{-27/2} = \frac{9 	imes 2}{27} = \frac{18}{27} = \frac{2}{3}$ Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = \frac{2}{3}$,the lines are coincident. Coincident lines have infinitely many solutions,therefore the system is consistent.

Examine graphically whether the pair of equations $2x + 4y = 9$ and $3x + 6y = \frac{27}{2}$ is consistent.

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