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Question

# The graphs of the equations $5x-15y=8\mathrm{and}3x-9y=\frac{24}{5}$ are two which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other

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Solution

## The correct option is (a). The given system of equations can be written as follows: $5x-15y-8=0\mathrm{and}3\mathrm{x}-9\mathrm{y}-\frac{24}{5}=0$ The given equations are of the following form: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 Here, a1 = 5, b1 = −15, c1 = −8 and a2 = 3, b2 = −9 and c2 = $-\frac{24}{5}$ ∴ $\frac{{a}_{1}}{{a}_{2}}=\frac{5}{3},\frac{{b}_{1}}{{b}_{2}}=\frac{-15}{-9}=\frac{5}{3}\mathrm{and}\frac{{c}_{1}}{{c}_{2}}=-8×\frac{5}{-24}=\frac{5}{3}$ ∴ $\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}$ The given system of equations will have an infinite number of solutions. Hence, the lines are coincident.

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