Question

what value of k the equations 8 x + 5 Y = 29 and K X + 10 Y = 215 has no solution​

Answer 1

Answer:

Step-by-step explanation:

If 8x+5y=29

Here

a1=8. b1=5 c1= -29

And in eq

Kx+10y =215

a2=k. b2=10 c2= -215

For no solution the equation must satisty

a1/a2 =b1/b2 ≠ C1/c2

8/k =5/10

Therefore

8 = 5k/10

8×10 =5k

K= 80/5

K =16

Hope this helps

Answer 2

AnswEr

The value of k is 16

GivEn

The equations are :

8x + 5y = 29

kx + 10y = 215

To FinD

The value of k

SoluTion

We know that if

$\sf a_{1}x +b _{1}y + c_{1} = 0 \: \: \: and \\ \sf a_{2}x + b_{2} y + c_{2} = 0$

are two equations having no solution then ,

$\sf \dfrac{a_{1}}{a_{2}} = \dfrac{b_{1}}{b_{2}} \neq \dfrac{c_{1}}{c_{2}}$

Thus ,

$\sf \implies \dfrac{8}{k} = \dfrac{5}{10} \neq \dfrac{29}{215}$

Taking the equal one we have,

$\sf \implies \dfrac{8}{k} = \dfrac{5}{10} \\\\ \sf \implies \dfrac{8}{k} = \dfrac{1}{2} \\\\ \sf \implies k = 2 \times 8 \\\\ \sf\implies k = 16$