Question

8. 8x + 5y =9, kx +10y =15.
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Answer 1

Answer:

Step-by-step explanation:

The given system of equations:

$8x + 5y = 9 \\ 8x + 5y - 9 = 0 ….(i) \\ kx + 10y = 15 \\ kx + 10y - 15 = 0 ….(ii)$

These equations are of the following form:

$a_{1} x+b_{1} y+c_{1} = 0, a_{2} x+b_{2} y+c_{2} = 0$

where, a₁ = 8, b₁ = 5, c₁ = -9 and a₂ = k, b₂ = 10, c₂ = – 15

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} } \\i.e. , \frac{8}{k} =\frac{5}{10} \neq \frac{-9}{-15} \\i.e.,\frac{8}{k} =\frac{1}{2} \neq \frac{3}{5} \\\frac{8}{k} =\frac{1}{2} and \frac{8}{k} \neq \frac{3}{5} \\k=16 and k\neq \frac{40}{3}$

Hence, the given system of equations has no solutions when k is equal to 16.