How do you solve the system of equations #3x + y = - 1# and #x = 3y - 7#?

1 Answer
Jim G.
Mar 8, 2017

#(-1,2)#

Explanation:

Since we are given #color(red)(x)=3y-7# we can substitute this directly into the other equation and solve for y.

#rArr3(3y-7)+y=-1#

distribute bracket.

#9y-21+y=-1#

#rArr10y-21=-1#

add 21 to both sides.

#10ycancel(-21)cancel(+21)=-1+21#

#rArr10y=20#

divide both sides by 10

#(cancel(10) y)/cancel(10)=20/10#

#rArry=2#

Substitute this value into #x=3y-7# to obtain x

#y=2tox=(3xx2)-7=6-7=-1#

#rArr(-1,2)" is the intersection of the 2 equations"#
graph{(y+3x+1)(y-1/3x-7/3)=0 [-10, 10, -5, 5]}

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