#5x+5y=40, x+y=8#. What is the solution?

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Answer 1 · 2018-03-04T21:01:27

#{8-t,t|tinRR}#

We have the following system of equations

#{: (5x+5y=40), (x+y=8) :}}#

Adding #-1"/"5# of eqn. #1# to eqn. #2# transforms the system into echelon form as

#{:(5x+5y=40),(0=0):}}#

To find solutions, we discard the degenerate equation and solve the other equation.

#5x+5y=40#

Since #y# is not a leading variable, we set it equal to an arbitrary variable, say #y=t# for #tinRR#.

We now solve for #x#

#5x+5t=40rArr5x=40-5trArrx=8-t#

So the set of solutions is #{8-t,t|tinRR}#