How do you solve the following system?: #5x + 2y =1 , 8x-9y= 12 #

1 Answer
Júlio B.
Jan 7, 2016

The solution set is: #S= {33/61, -52/61}#

Explanation:

Just isolate one constant(#x or y#) in one side on the equality and substitute in the other equality:
#5x +2y = 1 => 5x = 1 - 2y => x = (1-2y)/5#

Now, substitute:
#8 * (1-2y)/5 - 9y = 12# In order to take the dividing #5#, multiply the hole equation by #5#:
#cancel(5) * (8-16y)/cancel(5) - 5 * 9y = 60#
#8 - 16y - 45y = 60#
#-61y = 52 => y = - 52/61#

Now, just go back to the first equation and solve it:
#x = (1 - 2*(-52/61))/5 => x = (1 + 104/61)/5 => x = (61/61 + 104/61)/5 => (165/61)/5#
#x = (165/61)/5 = 165/61 * 1/5 = 33/61#

Then, the solution set is: #S= {33/61, -52/61}#

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