Question

find the value of b such that the system of equations
bx-15y=-20
4x+10y=-17
does not have a solution.
what is b=???

Answer 1

what is the condition for two lines not to have a solution?

Answer 2

b = - 6 ?

Answer 3

not sure what your question is. but what is b? that's all i need to know. and how to find it.

I've done this long time ago can't remember how to do these.

Answer 4

nice going dhatra :)i like ur approach :)

Answer 5

well, two lines are said to have a solution at the point of their intersection.
if the two lines are parallel, then they will not intersect, and hence will not have a solution.
two lines are parallel if
1. they have the same slope
2. they are separated by some distance.

Answer 6

why thank you, brackett. :)

Answer 7

dhatraditya. Explain to me, how would you solve for the variable b?

Answer 8

first lets rearrange each equation to the form y = mx+b

Answer 9

@beehive: for the equations to hav no solution, the lines must be parallel and hence their slope has to be same...therefore
u hav b/15=-4/10 and so u get, b=-6

Answer 10

yup, as brackett said.

Answer 11

brackett how did you get here?
b/15=-4/10 ????

Answer 12

i equated both the slopes

Answer 13

@ beehive: rearrange both the equations in the slope intercept form, ie
y = mx+b and post what you get.

Answer 14

do you know how to rearrange the equations, beehive?

Answer 15

yes i do. hold on a sec. I'm trying to get this straight in my head. i've done this like 4 years ago. forgot it all.

Answer 16

alright, whenever you are ready

Answer 17

for the first one. i got
\[y=\frac{-bx}{-15}+\frac{4}{3}\]
the second one i got.
\[y=-\frac{2}{5}x-\frac{17}{10}\]
this seem right?

Answer 18

right. that is correct.
now, for two equations expressed in the slope intercept form to be parallel, their slopes must be equal.
so -b/-15 = -2/5

Answer 19

well i understand you can rewrite the y=(-bx)/(15) to
\[y=\frac{-b}{15}x\]

Answer 20

ok i see. Thanks.

Answer 21

no, -bx/-15 = -1*bx/-1*15 = bx/15

Answer 22

you are welcome