How do you solve the following linear system: #-x + 4y = -8 , 3x - 5y = 3 #?

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Answer 1 · 2018-06-15T04:27:30

#x=-4# and #y=-3#.

Equation 1

#-x+4y=-8#

Equation 2

#3x-5y=3#

First solve Equation 1 for #x#.

Equation 3

#x=4y+8#

Substitute the expression for #x# from Equation 3 into Equation 2.

#3(4y+8)-5y=3#

Apply the distributive property

#12y+24-5y=3#

Combine like terms

#7y=-21#

Divide both sides of this equation by 7.

#y=-3#

Substitute this value for #y# into Equation 3 to determine the value of #x#.

#x=4(-3)+8=-12+8=-4#