Question

Find the value of k for which the equations:
2x+ky=1
3x-5y=7
1)has a unique solution
2)has no solution

Answer 1

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հίί ʍαtε_______✯◡✯
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_________________________
һєяє' ʏȏȗя ѧṅśwєя ʟȏȏҡıṅɢ ғȏя________
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✯the given question have no solution if,

✪
$\frac{a1}{a2} = \frac{b1}{b2} \: not \: \: equals \: to \: \frac{c1}{c2}$

✪ we have,

$\frac{a1}{a2} = \frac{b1}{b2}$


$\frac{2}{3} = \frac{k}{5}$

$- 10 = 3k$


$k \: = \frac{ - 10}{3}$

✪ we have,

$\frac{b1}{b2} = \frac{k} { - 5} = \frac{ - 10}{3 \times ( - 5)} = \frac{2}{3}$


✪ and,

$\frac{c1}{c2} = \frac{ - 1} { - 7} = \frac{1}{7}$

$clearly...... \frac{b1}{b2} \: \: not \: equals \: to \: \: \frac{c1}{c2}$

✪ so, the system will have no solution if,

$k = \frac{ - 10}{3}$

_________✪

$hope \: it \: helps$

✪ BRAINLY✪

Answer 2

the given question have no solution if,

✪

\frac{a1}{a2} = \frac{b1}{b2} \: not \: \: equals \: to \: \frac{c1}{c2}

a2

a1

=

b2

b1

notequalsto

c2

c1

✪ we have,

\frac{a1}{a2} = \frac{b1}{b2}

a2

a1

=

b2

b1

\frac{2}{3} = \frac{k}{5}

3

2

=

5

k

- 10 = 3k−10=3k

k \: = \frac{ - 10}{3}k=

3

−10

✪ we have,

\frac{b1}{b2} = \frac{k} { - 5} = \frac{ - 10}{3 \times ( - 5)} = \frac{2}{3}

b2

b1

=

−5

k

=

3×(−5)

−10

=

3

2

✪ and,

\frac{c1}{c2} = \frac{ - 1} { - 7} = \frac{1}{7}

c2

c1

=

−7

−1

=

7

1

clearly...... \frac{b1}{b2} \: \: not \: equals \: to \: \: \frac{c1}{c2}clearly......

b2

b1

notequalsto

c2

c1

✪ so, the system will have no solution if,

k = \frac{ - 10}{3}k=

3

−10