SOLUTION: 1/3x - 3/2y = 4 2x -by = 20 in this system of equations b is a constant. If the system has no solution, what is the value of b?

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Question 1097060: 1/3x - 3/2y = 4
2x -by = 20
in this system of equations b is a constant. If the system has no solution, what is the value of b?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Slopes are congruent.

%281%2F3%29%2F%283%2F2%29=2%2Fb

%281%2F3%29%282%2F3%29=2%2Fb
2%2F9=2%2Fb
highlight%28b=9%29



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cross%282=2%2Fb%29

cross%28b=1%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

1/3x - 3/2y = 4
2x -by = 20
in this system of equations b is a constant. If the system has no solution, what is the value of b?
b+%3C%3E+1, so IGNORE that, as usual. 

If done right, highlight_green%28matrix%281%2C3%2C+b%2C+%22=%22%2C+9%29%29

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
This system has no solution in only one case:


     If the coefficients of the second equation are proportional to coefficients of the first equation,
     BUT the right hand side terms ARE NOT proportional with that coefficient of proportionality.


     It is the same case when the straight lines of the equations are parallel,
     BUT not coincide.


The second equation coefficient "2" at "x" is 6 times the coefficient 1/3 at "x" in the first equation,
so the coefficient of proportionality must be 6:  %281%2F3%29%2A6 = 2.


Then -3%2F2 becomes  %28-3%2F2%29%2A6 = -9.


So, "b" must be equal 9.


Notice that the right side term 20 IS NOT 6 times 4.


Therefore,  b = 9 is the only value when the system HAS NO solution.


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See the lesson
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.