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) $$4x^2 + 10y^2 + 41x + 6y + 59=0$$ $$x - 2y - 1=0$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Solve each non-linear system of equations.
a) $$x^2 - x + y - 22=0$$ $$2x + y - 4=0$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Solve each non-linear system of equations.
a) $$x^2 + y^2 - 14x - 8y + 61=0$$ $$x^2 - 13y^2 - 14x + 104y - 163=0$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Solve each non-linear system of equations.
a) $$y^2 - 4x + 16y + 56=0$$ $$5x^2 + y^2 + 11x + 16y + 66=0$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Solve each non-linear system of equations.
a) $$6x^2 + 4xy - 6y^2=10$$ $$-x^2 - 3xy + y^2=3$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
a) $$\{(-3,-2)\}$$
Watch the Step by Step Video Solution
#2:
Solutions:
a) $$\{(-3,10),(6,-8)\}$$
Watch the Step by Step Video Solution
#3:
Solutions:
a) $$\{(9,4),(5,4)\}$$
Watch the Step by Step Video Solution
#4:
Solutions:
a) $$\{(-2,-8),(-1,-10),(-1,-6)\}$$
Watch the Step by Step Video Solution
#5:
Solutions:
a) $$\{(2,-1),(-2,1),(i,2i),(-i,-2i)\}$$
