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1 Answer
Jade
Mar 14, 2018

#sqrt117# units.
Refer to the explanation.

Explanation:

First, we will solve both these equations to find a coordinate which satisfies both of them.
From #5x+y=14# we get #y=14-5x#
now, substitute this value of #y# in the equation #2y+2x=12#
We get, #2(14-5x)+2x=12#
#28-10x+2x=12#
#28-8x=12#
#8x=16#
#x=16/8#
So, #x=2#
now, put this value of #x# in #y=14-5x#
#y=14-10#
#y=4#

So, the point of intersection is #(2,4)#

Now, the distance between #(2,4)# and #(11,-2)# can be found from distance formula.
#sqrt((2-11)^2+(4-(-2))^2)#
#sqrt((-9)^2 +6^2)#
#sqrt(81+36)#
#sqrt117 # units.

Hope this helps :)

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