How do you find the point of intersection for #x+y=3# and #2x-y= -3#?

2 Answers
Alan P.
Jun 26, 2015

The given lines intersect at #(0,3)#

Explanation:

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

add [1] and [2]
[3]#color(white)("XXXX")##3x = 0#
[4]#color(white)("XXXX")##x=0#

substituting #0# for #x# in [1]
#color(white)("XXXX")##0 + y = 3#
#color(white)("XXXX")##y=3#

Gió
Jun 26, 2015

I found the point of intersection of coordinates:
#x=0#
#y=3#

Explanation:

You basically solve the System of the two equations trying to find values of #x# and #y# that satisfy both equations simultaneously.
From the first you can isolate #x# as:
#x=3-y#
now you can substitute this #x# into the second equation and find #y# as:
#2(3-y)-y=-3#
#6-2y-y=-3#
#-3y=-9#
#y=3#
substitute back this value into the first equation to find #x#:
#x=3-3=0#

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