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