Solve the simultaneous equations
#2x+y=8.......................................(1)#
#4x^2+3y^2=52.......................(2)#
?
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# x= 3.5 and y =1 #
OR
#x = 2.5 and y = 3 #
#2x+y=8.......................................(1)#
#4x^2+3y^2=52.......................(2)#
(1) #=> y=8-2x#
(2) #=> 4x^2+3(8-2x)^2=52#
#=> 4x^2 +3(64 - 32x +4x^2) =52#
#=> 4x^2 + 192 - 96x + 12x^2 = 52#
#=> 16x^2 -96x + 140 = 0 #
#=> 4(4x^2 - 24x +35) = 0 #
#=> 4x^2 -24x +35 = 0#
Solving this quadratic equation, we get:
#=> (x-3.5)(x-2.5) = 0 #
#=> x= 3.5 or x = 2.5#
Substitute this value of #x# in equation (1):
Case 1: Taking #x= 3.5#
#=> 2x+y=8#
#=> 2(3.5) + y = 8#
# => y = 8-7 =1 #
OR
Case 2 : Taking #x= 2.5#
# 2(2.5) + y = 8#
# => y = 8- 5 = 3#
#therefore x= 3.5 and y =1 #
OR
#x = 2.5 and y = 3 #
#y=3 and x=5/2 or y=1 and x=7/2#
#2x+y=8#
#4x^2+3y^2=52#
#2x=8-y=>4x^2=(8-y)^2=color(blue)(64-16y+y^2)#
#color(blue)(64-16y+y^2)+3y^2=52#
#4y^2-16y+12=0#
dividing everything by 4(for symplifiying calculations):
#y^2-4y+3=0#
#y=(4+-sqrt(4^2-4*1*3))/2#
#y=(4+-sqrt(4))/2#
#y=(4+-2)/2#
#y=3 and x=5/2 or x=1 and x=7/2#
