Mathematics

Mathematics

Problem

A student writes the pair of equations 4x+3y=84x + 3y = 8 and 8x+6y=208x + 6y = 20. He concludes that the system has infinitely many solutions because the ratios of the coefficients of xx and yy are equal. Which statement correctly evaluates his conclusion? a) He is correct; the two lines are coincident. b) He is incorrect; the two lines intersect at exactly one point. c) He is incorrect; the two lines are parallel and have no solution because the constant terms do not satisfy the same ratio. d) He is correct; because multiplying the first equation by 2.52.5 gives the second equation, the lines coincide.

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