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

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Answer 1 · 2018-03-22T01:02:36

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

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.

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