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Find the k if equation have no solution (3k+1)x+3y=2,(k square +1)x+(k-2)y=5

Posted by Ram Singh Yadav 6 years, 4 months ago

1 answers

Sia ? 6 years, 4 months ago

Given linear equation is
(3k + 1)x + 3 y - 2 = 0 .......... (i)
(k² + 1)x + (k - 2)y - 5 = 0 ............ (ii)
Compare with a₁x + b₁y + c = 0 and a₂x + b₂y and c₂ = 0
a₁ = 3k + 1 , b₁ = 3 , c₁ = -2
and a₂ = k²+ 1 , b₂ = k - 2, c₂ = -5
The given system of equations will have no solution, if
{tex} \frac { a_1 } { a_2 } = \frac { b_1 } { b_2} \neq \frac { c_1 } { c_2 }{/tex}
{tex} \frac { 3 k + 1 } { k ^ { 2 } + 1 } = \frac { 3 } { k - 2 } \neq \frac { - 2 } { - 5 }{/tex}
{tex}\Rightarrow \quad \frac { 3 k + 1 } { k ^ { 2 } + 1 } = \frac { 3 } { k - 2 } \text { and } \frac { 3 } { k - 2 } \neq \frac { 2 } { 5 }{/tex}
Now, {tex}\frac { 3 k + 1 } { k ^ { 2 } + 1 } = \frac { 3 } { k - 2 }{/tex}
{tex}\Rightarrow{/tex} (3k + 1)(k - 2)=3(k² + 1)
{tex}\Rightarrow{/tex} 3k²- 5k - 2 =3k² + 3
{tex}\Rightarrow{/tex} -5k - 2 =3
{tex}\Rightarrow{/tex} -5k = 5
{tex}\Rightarrow{/tex} k = -1
Clearly, {tex}\frac { 3 } { k - 2 } \neq \frac { 2 } { 5 }{/tex} for k = -1.
Hence, the given system of equations will have no solution for k = -1.

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A thief after committing a theft, runs at a uniform speed of 50m/min. After 2 minutes, a policeman runs to catchbhim. He goes 60 m in 1st min and increases his speed by 5m/min every succeding min. After how many minutes, the policeman will catch the thief?

Posted by ☆ Pranal Rewatkar ☆ 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sithara Parwin 6 years, 10 months ago

Thief has a lead of 50*2 = 100m Relative distance covered by cop in 1st min = 60-50 = 10 Relative distance covered by cop in 2nd min = 65-50 = 15 Relative distance covered by cop in 3rd min = 70 -50 = 20 10, 15, 20 ... is an AP whose sum is 100 a= 10 , d = 5 Sum = 100 100 = n/2(2a + (n-1)d) = n/2(20 +(n-1)5 ) 100= n/2(20 + 5n -5) 200 = n(15 + 5n) divide by 5 40 = n(n + 3) n^2 + 8n - 5n - 40 =0 n(n+8) - 5(n+8)= 0 >> n = 5 as it cant be negative Therefore cop catches after 5 min + 2min (when cop was at rest) = 7min

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Posted by Ayush Bhatt 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Md Sohel 6 years, 10 months ago

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Posted by Md Sohel 6 years, 10 months ago

CBSE > Class 10 > Mathematics

3 answers

Nitin Dadhich 6 years, 10 months ago

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

1 answers

Nitin Dadhich 6 years, 10 months ago

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CBSE > Class 10 > Mathematics

0 answers

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Posted by Vansh Jangra 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

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CBSE > Class 10 > Mathematics

0 answers

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CBSE > Class 10 > Mathematics

1 answers

Lucky? Dangi 6 years, 10 months ago

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CBSE > Class 10 > Mathematics

1 answers

Nitin Dadhich 6 years, 10 months ago

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

2 answers

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Sahil Rajput 6 years, 10 months ago

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Posted by Neel Aslaliya 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

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Vishnu Vardhan 6 years, 10 months ago

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Posted by Sonia Saini 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Anushka ?? 6 years, 10 months ago

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Posted by Khushi Gupta 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

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Posted by Entertainment Kings 6 years, 10 months ago

CBSE > Class 10 > Mathematics

0 answers

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

1 answers

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Posted by Vijay Yadav 6 years, 10 months ago

CBSE > Class 10 > Mathematics

3 answers

Sonu Kumari 6 years, 10 months ago

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Ramesh Singh 6 years, 10 months ago

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Posted by Meraj Ahmad 6 years, 10 months ago

CBSE > Class 10 > Mathematics