- Define nonlinear system of equations.
- Determine the number of solutions that a system of nonlinear equations has when given a graph of the system.
- List the steps for solving systems of nonlinear equations using the substitution method.
- Solve systems of nonlinear equations.
- Use algebra to isolate a variable in a nonlinear equation.
- Quadratic Formula – A formula used to solve quadratic equations.
- The solutions to the quadratic equation are given by the formula .
- Isolate – To separate from others.
- To get the variable alone on one side of the equation or inequality.
- Nonlinear System of Equations – A group of nonlinear equations that have the same variables and are used together to solve a problem.
- The equations may be some combination of linear equations and nonlinear equations (all may be nonlinear, or only one may be nonlinear).
- System of Linear Equations – A group of linear equations that have the same variables and are used together to solve a problem.
- A linear equation can be written in the form y = mx + b.
- The graph of a linear equation is a straight line.
|Solutions of Nonlinear Systems of Equations|
Step 1: Isolate y in the 1st equation (divide by 3 on both sides).
Step 2: Substitute the y-value of “4x” into the 2nd equation.
Step 3: Square the 4x term.
Look for where the ellipse and hyperbola intersect.