SOLUTION: a-2b=9 2a-3b=4

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Question 1178089: a-2b=9 2a-3b=4
Found 4 solutions by mananth, MathTherapy, josgarithmetic, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
a-2b=9,
2a-3b=4
1.00 a + -2.00 b = 9.00


2.00 a + -3.00 b = 4.00 .............2
Eliminate b
multiply (1)by -3.00
Multiply (2) by 2.00
-3.00 a 6.00 b = -27.00
4.00 a -6.00 b = 8.00
Add the two equations
1.00 a = -19.00
/ 1.00
a = -19.00
plug value of a in (1)
1.00 a + -2.00 b = 9.00
-19.00 + -2.00 b = 9.00
-2.00 b = 28.00
b = -14.00
Ans a = -19.00
b = -14.00


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

a-2b=9 2a-3b=4
DON'T ever solve a problem like this the way the other person did! It's just UNHEARD of and ridiculously UNNECESSARY!

a - 2b = 9 ----- eq (i)

2a - 3b = 4 ---- eq (ii)

2a - 4b = 18 --- Multiplying eq (i) by 2 ------ eq (iii)

 ----- Subtracting eq (iii) from eq (ii)

Substitute - 14 for b in either eq (i) or (ii) to get the value of "a." 

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
 
a-2b=9 2a-3b=4
















E1-E2:











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Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .





            The solution by @josgarithmetic giving the answer   a= 37,   b= -14  is  INCORRECT.





            I came to bring you the correct solution.








Your starting equations are


     a - 2b = 9     (1)

    2a - 3b = 4     (2)


To solve the system, express a = 2b + 9 from the first equation and substitute it into the second equation, 
replacing  "a" there.  You will get


    2*(2b+9) - 3b = 4

    4b + 18 - 3b = 4

    4b - 3b = 4 - 18 

       b    = -14.


Now from equation (1),  a = 2b + 9 = 2*(-14) + 9 = -28 + 9 = -19.


ANSWER.  a= -19;  b= -14.


CHECK.  To check the solution, substitute the found values "a" and "b" into the original equations.





Solved (correctly).





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For your safety,  ignore the post by @josgarithmetic.







 

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