Question

if the pair of equations 2x+3y=7 and kx+9/2y=12 has no solution, then the value of k is​

Answer 1

Answer:

Step-by-step explanation:

Have no solution means that the lines are parallel

i.e.,a1/a2 is equal to b1/b2 is not equal to c1/c2

In the first equation ,

2x + 3y =  7 or 2x + 3y -7=0

a1 = 2 , b1 = 3 ,  c1 = (-7)

and in the second equation

kx +9/2y = 12 or kx +9/2y -12 = 0

a2 = k , b2 = 9/2 and c2 = (-12)

therefore a1/a2 = 2/k,

b1/b2 = 3/9/2  

=>  3/9  * 2/1

=>  6/9

=>  2/3

c1/c2 = (-7)/(-12)

therefore k = 3

as a1/a2 = b1/b2

i.e.,  2/k = 2/3

k=3

I hope that this answer may help u

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sinQ /cosQ

=tanQ

Answer 2

Given pair of equations are

$2x + 3y - 7 = 0 \\ kx + (9 \div 2)y - 12 = 0$

Given that the pair of equations has no solution.

This simply means that the given pair of equations are parallel.

The condition for pair of equations to be parallel is

$a1 \div a2 = \:b1 \div b2 \: not \: equal \: to \: c1 \div c2$

Pair of equations are represented by the form

$a1x + b1y + c = 0 \\ a2x + b2y + c = 0$

Here,

$a1 = 2 \\ b1 = 3 \\ c1 = - 7 \\ a2 = k \\ b2 = 9 \div 2 \\ c2 = - 12$

By substituting these values in the condition of parallel lines.

$a1 \div a2 = b1 \div b2 \\ 2 \div k = 3 \div (9 \div 2) \\ 2 \div k = 6 \div 9 \\ 2 \div k = 2 \div 3 \\ k = 3$

Therefore, the value of k is

$k = 3$

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