SOLUTION: 3a+5b=3,a+2b=13

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Question 1208192: 3a+5b=3,a+2b=13
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
3a+5b=3, a+2b=13
~~~~~~~~~~~~~~~~~~~~~~~ 

They want you solve this system of two equations

    3a + 5b =  3,     (1)

     a + 2b = 13.     (2)


There are different methods for it.


I will show here the SUBSTITUTION method.


From equation (2), express  a = 13 - 2b.  

Substitute this expression for "a" into equation (1).  You will get

    3*(13-2b) + 5b = 3.


It is a single equation for a single unknown "b". 
Simplify it and find  "b"

    39 - 6b + 5b = 3,

    39 - b = 3,

    39 - 3 = b,

    b   = 36.


Substitute this value b = 36 into equation (2) and find "a"

    a + 2*36 = 13,

    a + 72 = 13,

    a = 13 - 72 = -59.


Thus a= -59, b= 36 is the unique solution to the original system.    ANSWER 


You may check that each equation (1) and (2) becomes an identity, when you substitute a= -59, b= 36 there.

This check confirms that the found values are correct solutions.

Solved.



Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!


Elimination Method may be a good choice.

Multiply entire second equation by 3.


From this, add negative of first equation to second equation.





This value for b could be used for substituting into the original second
equation to find a.
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