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  • For all real values of c, the pair of equations x– 2y = 8 5x – 10y = c have a unique solution. Justify whether it is true or false.

For all real values of c, the pair of equations x– 2y = 8, 5x – 10y = c have a unique solution. Justify whether it is true or false.

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Solution:
Equation are x – 2y = 8
5x – 10y = c
Here a1 = 1, b1 = –2, c1 = –8
a2 = 5, b2 = –10, c2 = –c

\frac{a_{1}}{a_{2}}= \frac{1}{5};\frac{b_{1}}{b_{2}}= \frac{-2}{-10}= \frac{1}{5};\frac{c_{1}}{c_{2}}= \frac{-8}{-c}= \frac{8}{c}
For unique solution \frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}} but here \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}

Hence the given statement is false.

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infoexpert27

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