How do you solve the following system?: # -2x +5y =-6 , 5x +6y = -1#

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Answer 1 · 2016-07-11T10:31:06

#x = 31/37, y = -32/37#

We can solve for #y# first by multiplying the first equation by #5# and the second equation by #2#:

#5(-2x + 5y) = (-6)5# and #2(5x + 6y) = (-1)2#

Then we add the two equations, resulting in:

#25y + 12y = -32#, and therefore, #37y = -32#

We divide both sides by #37#, so #y = -32/37#

To solve for #x#, we multiply the first equation by #-6# and the second equation by #5#:

#-6(-2x + 5y) = -6(-6)# and #5(5x + 6y) = 5(-1)#

Then we add the two equations, resulting in:

#12x + 25x = 31#, and therefore, #37x = 31#

We divide both sides by #37#, so #x = 31/37#

You can verify these answers by substituting #31/37# for #x# and #-32/37# for #y#:

#-2(31/37) + 5(-32/37) = -62/37 - 160/37 = -222/37 = -6#