About Solving Non Linear Systems of Equations:

When we look at non-linear systems of equations, at least one equation of the system is non-linear. To solve a non-linear system of equations, we rely on the substitution method, the elimination method, or a combination of both methods.


Test Objectives
  • Demonstrate the ability to solve a non-linear system using substitution
  • Demonstrate the ability to solve a non-linear system using elimination
  • Demonstrate the ability to solve a non-linear system using a combination of the substitution and elimination methods
Solving Non Linear Systems of Equations Practice Test:

#1:

Instructions: Solve each non-linear system of equations.

a) $$4x^2 + 10y^2 + 41x + 6y + 59 = 0$$ $$x - 2y - 1 = 0$$


#2:

Instructions: Solve each non-linear system of equations.

a) $$x^2 - x + y - 22 = 0$$ $$2x + y - 4 = 0$$


#3:

Instructions: Solve each non-linear system of equations.

a) $$x^2 + y^2 - 14x - 8y + 61 = 0$$ $$x^2 - 13y^2 - 14x + 104y - 163 = 0$$


#4:

Instructions: Solve each non-linear system of equations.

a) $$y^2 - 4x + 16y + 56 = 0$$ $$5x^2 + y^2 + 11x + 16y + 66 = 0$$


#5:

Instructions: Solve each non-linear system of equations.

a) $$6x^2 + 4xy - 6y^2 = 10$$ $$-x^2 - 3xy + y^2 = 3$$


Written Solutions:

#1:

Solutions:

a) $$\{(-3,-2)\}$$


#2:

Solutions:

a) $$\{(-3,10),(6,-8)\}$$


#3:

Solutions:

a) $$\{(9,4),(5,4)\}$$


#4:

Solutions:

a) $$\{(-2,-8),(-1,-10),(-1,-6)\}$$


#5:

Solutions:

a) $$\{(2,-1),(-2,1),(i,2i),(-i,-2i)\}$$