| For what value of k, the following equations have no solution? \[9x+4y=9\,;\,\,7x+ky=5\] [SSC (CGL) 2014] |
A) 3
B) 4.7
C) 28/9
D) 9/28
Correct Answer: C
Solution :
(c)| Given equations, |
| \[9x+4y=9\] |
| and \[7x+ky=5\] |
| Standard equations |
| \[{{a}_{1}}x+{{b}_{1}}y={{c}_{1}}\] |
| and \[{{a}_{2}}x+{{b}_{2}}y={{c}_{2}}\] |
| We know that, equations to have no solution the condition is \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\] |
| Now, comparing given equations with standard equations, |
| we get \[\frac{9}{7}=\frac{4}{x}\]\[\Rightarrow \]\[k=\frac{4\times 7}{9}=\frac{28}{9}\] |
| Hence, \[k=\frac{28}{9}\] for the equations to have no solution. |
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