Question

For what value of k will the equations 3x - 4y = 5 and 9x - 12y = k be consistent?​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

3

Explanation:

Consistent means that the given pair of equations have solutions. It does not matter whether the ratio of variables is equal or not.

A pair of linear equations will be consistent only when they satisfy the following conditions:-

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }=\frac{c_{1} }{c_{2} }$

     or

$\frac{a_{1} }{a_{2} }\neq \frac{b_{1} }{b_{2} }$

Given:-

Equations: 3x-4y=5 and 9x-12y=k

Step by step explanation:-

We have,

$a_{1} =3,b_{1} =-4,c_{1} =5\\a_{2}=9,b_{2} =-12,c_{2} =k$

$\frac{a_{1} }{a_{2} }=\frac{3}{9} =\frac{1}{3} \\\frac{b_{1} }{b_{2} }=\frac{-4}{-12} =\frac{1}{3}$

$Since, \frac{a_{1} }{a_{2} }=\frac{b_{1} }{b_{2} }$ first rule will apply here,

∴$\frac{a_{1} }{a_{2} }=\frac{c_{1} }{c_{2} }$

⇒ $\frac{1}{3}=\frac{5}{k}$

⇒k = 5×3

⇒k = 15

Hence the value of k = 15