Question 454327
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Solve the linear system by using substitution. 3x+2y=5, 5x-9y=-4
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        In his post, @mananth makes 16 tons incorrect calculations.

        A true solution, which I provide below, has nothing in common with the @mananth writing.



<pre>
Your starting equations are 

    3x + 2y = 5,     (1)

    5x - 9y = -4.    (2)


From equation (1), express  y = {{{((-3x)+5)/2}}}  and substitute it into equation (2), replacing 'y' there

    5x - {{{9*((-3x)+5)/2}}} = -4.


Multiply both sides by 2 to rid of the numerator

    10x - 9*((-3x)+5) = -8.


Simplify and find 'x' from this equation

    10x + 27x - 45 = -8

    37x = -8 + 45

    37x = 37

      x = 37/37 = 1.


Now substitute x = 1 into equation (1) and find 'y'

    3*1 + 2y = 5  --->  2y = 5 - 3 = 2  --->  y = 2/2 = 1.


<U>ANSWER</U>.  x = 1,  y = 1.
</pre>

Solved.