How do you solve the following system: #-29=5y-3x, 5x+2y=12 #?

1 Answer
Jake M.
Mar 22, 2018

#x = 118/31# and # y = -109/31#

Explanation:

We can eliminate a variable by subtracting out an equation.

For example, let's take 3 times the second plus five times the first:

#3(5x+2y = 12) implies 15x + 6y = 36 #
#5(-3x + 5y = -29) implies -15x + 25y = -145#
Adding them together,
#31y = -109 implies y = (-109)/31 #

We can now plug this into our second equation from before and get #x#:
#5x + 2((-109)/31) = 12 implies 5x = 12 + 218/31 = 590/31 #
#x = 118/31 #

Thus we have our answer.

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