Question

6. Find the value of k for which the following pair of linear equation

has no solution : kx + 2y = 5 & 8x + ky = 20​

Answer 1

Answer:

no solution a1/a2=b1/b2 is not equal to c1/c2

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Answer 2

The value of k  is 4 and - 4.

Step-by-step explanation:

Given:

The  linear equation $kx+2y=5$.

The  linear equation $8x+ky=20$.

To Find:

The value of k.

Formula Used:

A system of linear equations $px+qy+r=0$  and $sx+ty+u=0$ will have no solution if $\frac{p}{s} =\frac{q}{t} \neq \frac{r}{u}$    ---------------- formula no.01.

Solution:

As given-the  linear equation $kx+2y=5$.

Comparing with linear equation $px+qy+r=0$,

$p=k , \ q=2 \ and\ r=-5$

As given-the  linear equation $8x+ky=20$.

Comparing with linear equation $sx+ty+u=0$,

$s=8 , \ t=k \ and\ u=-20$

Putting the value of  p,q ,s and t in formula no.01.

$\frac{p}{s} =\frac{q}{t}$

$\frac{k}{8} =\frac{2}{k}$

$k^{2} =16$

$k=4 \ and -4$

Thus,the value of k  is 4 and - 4.

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