How do you solve the system of equations: y = -3x + 5 and 5x - 4y = -3?

1 Answer
Alan P.
Aug 7, 2015

#(x,y) = (1,2)#

Explanation:

[1]#color(white)("XXXX")##y=-3x+5#
[2]#color(white)("XXXX")##5x-4y=-3#

Since [1] gives us an expression for #y# in terms of #x#
the obvious solution method would be to substitute this expression for #y# in [2]
[3]#color(white)("XXXX")#5x-4(-3x+5)=-3#

Simplifying the left side
[4]#color(white)("XXXX")##17x-20 = -3#

Adding 20 to both sides:
[5]#color(white)("XXXX")##17x = 17#

Dividing by 17
[6]#color(white)("XXXX")##x=1#

Substituting #1# for #x# back in [1]
[7]#color(white)("XXXX")##y = -3(1)+5#

Simplifying
[8]#color(white)("XXXX")##y=2#

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