How do you solve the simultaneous equations # y+2x=6# and #y=4/x#?

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Answer 1 · 2018-03-09T13:51:14

The solution sets are #(1,4)# and #(2,2)#

We have #y+2x=6# and #y=4/x#. Input the second equation into the first:

#4/x+2x=6#

#(2x^2+4)/x=6#

#2x^2+4=6x#

#2x^2-6x+4=0#

#x^2-3x+2=0#

#x^2-x-2x+2=0#

#x(x-1)-2(x-1)=0#

#(x-1)(x-2)=0#

#x=1,2#

Inputting the first value into equation one:

#y+2*1=6#

#y+2=6#

#y=4#

Inputting the second value into equation one:

#y+2*2=6#

#y+4=6#

#y=2#

The solution sets are #(1,4)# and #(2,2)#.