Question #1f49f

1 Answer
Jan 19, 2018

The points of intersection occur at value(s) of #x# where both equations give the same #y# value.

So we want #3/2x-8# to be the same as #-x+7#.

We need to solve:

#3/2x-8 = -x+7#

#3/2x+x=7+8#

#5/2x=15#

#2/5(5/2x) = 2/5(15)#

#x = 6# #" "# (Also see Note below>0

At #x = 6#, the first equation gives us #y = -(6)+7 = 1# and the second equation gives us #y = 3/2(6)-8 = 9-8 = 1#.

The point of intersection is #(6,1)#

Note

Another way to solve #3/2x-8 = -x+7#

If we want to avoid fractions, we can begin by multiplying both sides of the equation by a common denominator. In this case #2#

#2(3/2x-8) = 2(-x+7)#

#3x-16 = -2x+14#

#3x+2x = 14+16#

#5x=30#

#x=6#

When #x = 6# either equation gives us #y=1# so

the point of intersection is #(6,1)#.