How do solve the following linear system?: # 5x+2y=4 , y=-3x+4 #?

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Answer 1 · 2018-03-11T22:54:14

#x=4, y=-8#

#5x+2y=4#
#y=-3x+4#

Since the second function already has the y term isolated, plug it in for y in the first function to solve for x

#5x+2(-3x+4)=4# (Distribute the 2)

#5x-6x+8=4# (Combine like terms)

#-x+8=4# (Subtract 8 from both sides)

#-x=-4# (Divide both sides by -1)

#x=4#

Now that you found the x variable, plug it into either equation to find y

#y=-3(4)+4# (Distribute -3)

#y=-12+4# (Find the difference/sum)

#y=-8#

Check your answer by plugging it back into either of the original equations

#5(4)+2(-8)=4#

#20+(-16)=4#

#4=4#

This is how you solve by substitution