6x+y^2=10 and 3x-y=5 find all solutions and determine whether or not the system is linear or nonlinear?

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Answer 1 · 2018-08-05T23:26:50

#(1,-2)# and #(5/3,0)#
The system will be nonlinear because it includes a quadratic equation.

This is a system of equations, so solving one term one in terms of the other will allow you to find the solution

#-y=-3x+5#
#y=3x-5#

Then plug in the value of #y# into the first equation

#6x+(3x-5)^2=10#

Solve for #x#

#6x+9x^2-30x+25=10#
#9x^2-24x+15=0#
#3(x^2-8x+5)=0#
#3(x-1)(x-5/3)=0#

#x=1, 5/3#

Now that we know the x coordinates of the solutions, we can plug them into one of the equations to solve for the y coordinates

#3(1)-y=5#
#y=-2#

#3(5/3)-y=5#
#y=0#