Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Solving a linear and a nonlinear equation together
Solve systems involving linear and nonlinear relations
Problem types
- Solve a line and parabola system
- Solve or classify a system of a circle and a line
Builds on
- Where a line meets a parabola
- Solving quadratic equations
- Systems of linear equations
- Linear growth against exponential growth · Useful idea
Where a linear and an exponential model are equal is a solution of a system with a curve.
- Solving radical equations · Useful idea
Solving a radical equation is finding the intersection of a root curve with another curve, and extraneous solutions are points that do not lie on both.
- Why elimination keeps the same solutions · Earlier idea
Eliminating a variable from two equations works for a system with a curve, leaving one equation in the remaining variable.
- Systems that model two constraints · Earlier idea
Setting up a system from a situation extends to systems with a curve, where solutions are intersection points.
Leads to
- How many times a line meets a curve
- Quadratic, rational, and exponential constraints · See it applied
The break-even point of a quadratic and a linear model is the solution of a nonlinear system.
- Conic sections and their equations · See it applied
Finding where a line meets a circle or other conic solves a nonlinear system.
Related skills
- Approximating a solution from a graph · Related idea
Substitution gives exact intersections when the equation can be solved by factoring. A table of values approximates intersections that algebra cannot give simply.
- Completing the square · Shared foundations
- Operations on matrices · Shared foundations
- A system written as a matrix equation · Shared foundations
Open the interactive map to explore lessons and skill connections.