Question #d5b6d

2 Answers
Sep 29, 2017

#(5,1)#

#(-11,67/3)#

Explanation:

#4x+3y=23---(1)#

#2x^2-9y=41---(2)#

normally with these we would rearrange one eqn for one variable and substitute into eh other eqn.

Here, however we can quickly eliminate one of the variables as follows

#xx(1)" by " 3#

#12x+9y=69---(1a)#

#2x^2-9y=41---(2)#

ADD

#2x^2+12x=110#

#=>x^2+6x-55=0#

the rearranging is left as an exercise for the reader

#(x+11)(x-5)=0#

#=>x=5" or "x=-11#

#x=5#

using #(1)#

#4xx5+3y=23#

#=>3y=3#

:.y=1#

one soln# (5,1)#

#x=-11#

#4x+3y=23#
-44+3y=23#

#3y=67#

#:.y=67/3#

other soln

#(-11,67/3)#

Sep 29, 2017

#x=5,-11#
#y=1,-67/3#

Explanation:

#4x+3y=23#
#3y=-4x+23#
#9y=3(-4x+23)=-12x+69#
Substituting the value of 9y in the second equation,
#2x^2+12x-69=41#
#2x^2+12x-110=0#
#2x^2-10x+22x-110=0#
#2x(x-5)+22(x-5)=0#
#(2x+22)(x-5)=0#
#x=5, -11#
#4x+3y=23#
#3y=-4x+23#
When #x=5#, #3y=-20+23=3# or #y=1#
When #x=-11#, #3y=44+23=67#; #y=67/3#