MATHEMATICS · Single correct · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
A student writes the pair of equations 4x+3y=8 and 8x+6y=20. He concludes that the system has infinitely many solutions because the ratios of the coefficients of x and y 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 2.5 gives the second equation, the lines coincide.