anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I still didn't understand the question dear do you want to know what will a = ? and b=2? to satisfy the given conditions?
anonymous
  • anonymous
b = ?*
anonymous
  • anonymous
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 = )

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More answers

anonymous
  • anonymous
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.
anonymous
  • anonymous
hmmm, not sure about (b) though >_< lol
anonymous
  • anonymous
all right lol thanks = )
anonymous
  • anonymous
np :) sorry for the mess >_<
anonymous
  • anonymous
it's all good ^_^
dumbcow
  • dumbcow
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
angela210793
  • angela210793
how abt: x+2y= 3----> y=(3-x)/2 \[x \neq3 cause 3-3/2=0\]
anonymous
  • anonymous
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 \[a1/a2=b1/b2=c1/c2\]
anonymous
  • anonymous
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 \[a/b \neq 1/2\]

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