Question

If 2x + 3y = 6 and ax + 9y = c have no common solution, what is the value of a?

Answer 1

Step-by-step explanation:

here is your answer to the question

Answer 2

$Compare \: given \:pair \:of \: equations$

$2x + 3y - 6 = 0 \: and \: ax+9y - c = 0 \:with$

$a_{1}x+ b_{1}y + c_{1} = 0 \:and$

$a_{2}x+ b_{2}y + c_{2} = 0, we \:get$

$a_{1} = 2 , b_{1} = 3, \: c_{1} = -6$

$and \: a_{2} = a , b_{2} = 9, \: c_{2} = -c,\:we \:have$

$\boxed{\pink{ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} }}$

$\blue{ ( Given \: no \: Common \: solution )}$

$\implies \frac{2}{a} = \frac{3}{9}$

$\implies \frac{a}{2} = \frac{9}{3}$

$\implies a = \frac{9}{3} \times 2$

$\implies a = 3 \times 2$

$\implies a = 6$

Therefore.,

$\red{ Value \:of \: a } \green { = 6 }$

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