Question

If the equations x+5y=7 & 4x+20y= -k represent coinciding straight lines. Then the value of k is​

Answer 1

Answer:

Step-by-step explanation:

if two equation can be transformed to one form and they are equal then the lines are coinciding.

suppose you have two equations in the form of

a1x+b1y+c1=0and

a2x+b2y+c2=0

then for lines to be coinciding

a1/a2=b1/b2=c1/c2

1/4=5/20=-7/k

therefore

k=-28 Ans

Answer 2

Answer :

The value of k is -28

Given :

The equations are :

x + 5y = 7

4x + 20y = -k

These two equations represent coinciding straight line

To Find :

The value of k

Solution :

Considering the equations as :

x + 5y = 7 ........(1)

4x + 20y = -k .........(2)

Thus we have

$\sf{a_{1} = 1 \: \: , b_{1} = 5, \: \: c_{1}= 7 }$

$\sf{a_{2} = 4 \: \: , b_{2}=20, \: \: c_{2} = -k}$

Since , the equations (1) and (2) represent coinciding straight line so the equations has infinitely many solutions . Thus the coefficients of both the equations will be :

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

$\sf \longrightarrow \dfrac{1}{4} = \dfrac{5}{20} = \dfrac{7}{ - k}$

Taking one pair out as equation we have :

$\sf \implies\dfrac{1}{4} = \dfrac{7}{ - k} \\ \sf \implies - k = 7 \times 4 \\ \sf \implies - k = 28 \\ \bf \implies k = - 28$