About Nonlinear Systems of Equations:

A nonlinear system of equations is one in which at least one equation of the system is not linear. Most often, we will solve such a system using substitution, elimination, or a combination of the two.


Test Objectives
  • Demonstrate the ability to solve a nonlinear system of equations
Nonlinear Systems of Equations Practice Test:

#1:

Instructions: Solve each system.

$$a)\hspace{.2em}5x^2 + 3y^2 + 22x + 2y + 23=0$$ $$x - 2y=0$$

$$b)\hspace{.2em}-10x^2 + 10y^2 - 23x - 6y - 34=0$$ $$x + 2y - 2=0$$


#2:

Instructions: Solve each system.

$$a)\hspace{.2em}x^2 + y^2 - 24x - 16=0$$ $$3x - y=-4$$

$$b)\hspace{.2em}2x^2 + y^2 - 14x - 13=0$$ $$x + y + 4=0$$


#3:

Instructions: Solve each system.

$$a)\hspace{.2em}-x^2 + y^2 - 4y - 5=0$$ $$x^2 + 5y^2 + 16y + 11=0$$

$$b)\hspace{.2em}-x^2 + y^2 + 12x - 3y - 34=0$$ $$-x^2 + y^2 + 12x + 3y - 46 = 0$$


#4:

Instructions: Solve each system.

$$a)\hspace{.2em}-2y^2 + x + 28y - 79=0$$ $$4y^2 + x - 56y + 161=0$$

$$b)\hspace{.2em}x^2 + y^2 - 18x - 2y + 18=0$$ $$18x^2 - y^2 - 172x + 2y + 153=0$$


#5:

Instructions: Solve each system.

$$a)\hspace{.2em}xy=-15$$ $$4x + 3y=3$$

$$b)\hspace{.2em}2x + |y|=4$$ $$x^2 + y^2=5$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}(-2, -1)$$

$$b)\hspace{.2em}(-2, 2)$$


#2:

Solutions:

$$a)\hspace{.2em}(0, 4)$$

$$b)\hspace{.2em}(1, -5)$$


#3:

Solutions:

$$a)\hspace{.2em}(0, -1)$$

$$b)\hspace{.2em}(6, 2)$$


#4:

Solutions:

$$a)\hspace{.2em}(-1, 10), (-1, 4)$$

$$b)\hspace{.2em}(1, 1), (9, 9), (9, -7)$$


#5:

Solutions:

$$a)\hspace{.2em}(-3, 5), \left(\frac{15}{4}, -4\right)$$

$$b)\hspace{.2em}(1, -2), (1, 2)$$