Question

Find conditions on a amd b such that the system of linear equations has (a) no solutions, b) unique solution c) infinite many solutions

x+2y= 3 and ax + by = -9

Answer 1

I still didn't understand the question dear

do you want to know what will a = ? and b=2? to satisfy the given conditions?

Answer 2

b = ?*

Answer 3

lool, it's like for example, for a), if the two linear equations are parallel to each other, than there's no solutions at all, and the questions is to find the a and b, which value should we take in order to have *no solutions* lol = )

Answer 4

alright then first write the equation in slope intercept form :

y = -x/2 + 3

in this case m = -1/2 so (a) should be -1/2 , parallel = means same slope.
Perpendicular = means the reciprocal of the slope.

Answer 5

hmmm, not sure about (b) though >_< lol

Answer 6

all right lol thanks = )

Answer 7

np :) sorry for the mess >_<

Answer 8

it's all good ^_^

Answer 9

yes the slope is -1/2 and to have no solution they need to have same slope
however, a does not represent the slope
put 2nd equation in slope-intercept form
y = (-a/b)x -9/b
-a/b is slope
-a/b = -1/2
a/b = 1/2
a=1 and b=2
or
a=2, b=4 ...


part c)
infinite solutions means they are the same line
so same slope of -1/2 again
but now the y_intercepts must be the same
y = -x/2 +3/2 , y = (-a/b)x -9/b
-9/b = 3/2
3b = -18
b = -6
and
a/b = 1/2
a/-6 = 1/2
a = -3

part b)
a and b can be any other numbers except those used in part a and c
if 2 lines are distinct and not parallel then they must intersect at some point
so
a=3
b=5

Answer 10

how abt: x+2y= 3----> y=(3-x)/2
\[x \neq3 cause 3-3/2=0\]

Answer 11

let two equations be a1x+b1y=c1 & a2x+b2y=c2.
they have uniq solutions if \[a1/a2\neq b1/b2\]has no solutions if \[a1/a2=b1/b2\neq c1/c2\]has infinite solutions if \[a1/a2=b1/b2=c1/c2\]

Answer 12

so from your given equations for infinite solutions 1/a=2/b=3/-9
a=-3, b=-6.

for no solutions \[1/a =2/b \neq3/-9\] \[b/a=2 \] \[a \neq -3 , b\neq -6\]
for unique solutions \[a/b \neq 1/2\]