Is #(2,5)# a solution to the system of equations #6x + y = 17# and #3x + 2y = 16#?

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Answer 1 · 2017-03-04T17:59:37

Because the pair is a solution for both equations it is therefore a solution for the system of equations.

First, substitute #2# for #x# and #5# for #y# in the first equation and determine if this pair is a solution:

#6x + y = 17# becomes:

#(6 xx 2) + 5 = 17#

#12 + 5 = 17#

#17 = 17#

Because the pair is a solution for the first equation we must do the same substitution and solution for the second equation:

#3x + 2y = 16# becomes:

#(3 xx 2) + (2 xx 5) = 16#

#6 + 10 = 16#

#16 = 16#