### 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

#1:

Instructions: Solve each non-linear system of equations.

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

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#2:

Instructions: Solve each non-linear system of equations.

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

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#3:

Instructions: Solve each non-linear system of equations.

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

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#4:

Instructions: Solve each non-linear system of equations.

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

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#5:

Instructions: Solve each non-linear system of equations.

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

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Written Solutions:

#1:

Solutions:

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

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#2:

Solutions:

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

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#3:

Solutions:

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

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#4:

Solutions:

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

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#5:

Solutions:

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