Question

write down Assignment the Condition - I for which the following pair linea equation have no Solution, hence find the value of k.
2x-3y = 6 3x - (K-2)y=9​

Answer 1

Answer:

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Step-by-step explanation:

Given pair of linear equations:

2x+3y=9 ---(1)

6x+(k-2)y=3k-2 ----(2)

Compare these equations with

a1x+b1y=c1 and a2x+b2y=c2

we get

\begin{gathered} a_{1}=2, b_{1}=3\\a_{2}=6,b_{2}=k-2 \end{gathered}

a

1

=2,b

1

=3

a

2

=6,b

2

=k−2

Now ,

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

a

2

a

1

=

b

2

b

1

/* Given linear equations have no solution */

\implies \frac{2}{6}=\frac{3}{k-2}⟹

6

2

=

k−2

3

Do the cross multiplication, we get,

\implies 2(k-2)=6\times 3⟹2(k−2)=6×3

\implies k-2 = \frac{6\times3}{2}⟹k−2=

2

6×3

\implies k-2=9⟹k−2=9

\implies k = 9+2⟹k=9+2

\implies k = 11⟹k=11

Therefore,

k = 11

••••

Answer 2

Step-by-step explanation:

Answer

2x+3y=9,6x+(k−2)y=(3k−2)

These given equations are in the form:

a

1

x+b

1

y+c

1

=0 and

a

2

x+b

2

y+c

2

=0

Where

a

1

=2,b

1

=3 and c

1

=9

a

2

=6,b

2

=(k−2) and c

2

=(3k−2)

a

2

a

1

=

6

2

,

b

2

b

1

=

k−2

3

,

c

2

c

1

=

3k−2

9

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Therefore, the system has no solution.

Now,

2/6=3/(k−2)

2k−4=18

or k=11

Since

b

2

b

1



=

c

2

c

1

3/9



=9/31

Which is true. The value of k is 11.