Solve a non-linear system of equations

Learning Objectives Identify a system of equations as linear or non-linear. Solve a non-linear system of equations using the substitution method. Solve a non-linear system of equations using the elimination method. Interpret the solutions of a non-linear system graphically as the points of intersection of their curves. Solve systems involving a line and a conic section (e.g., parabola, circle). Solve systems involving two conic sections (e.g., two circles, a circle and a hyperbola). Determine the number of possible real solutions for a given non-linear system. Ever wonder how GPS pinpoints your location? 🛰️ It involves solving a system of equations where signals from satellites form intersecting spheres! In this tutorial, you'll move beyond straight lines and learn h...

TermDefinitionExample Non-Linear System of EquationsA set of two or more equations, where at least one equation's graph is not a straight line. The solution is the set of ordered pairs (x, y) that satisfies all equations in the system.The system containing y = 2x + 3 (a line) and x² + y² = 9 (a circle) is a non-linear system. Point of IntersectionThe graphical representation of a solution to a system. It is the coordinate point where the graphs of the equations cross each other.The graphs of y = x² and y = x + 2 intersect at the points (-1, 1) and (2, 4), which are the two solutions to the system. Substitution MethodAn algebraic technique where you solve one equation for a single variable and then substitute that expression into the other equation to eliminate one variable.For the sy...

The Substitution Method Steps 1. Isolate a variable in one equation. 2. Substitute the resulting expression into the other equation. 3. Solve the new equation. 4. Back-substitute the result(s) into the isolated equation to find the corresponding values of the other variable. This is the most reliable method, especially when one of the equations is linear or can be easily solved for a variable like y or x². The Elimination Method Steps 1. Align like terms in both equations. 2. Multiply one or both equations by constants to make the coefficients of one variable opposites. 3. Add the equations to eliminate that variable. 4. Solve the resulting equation and back-substitute. This method is most efficient when both equations have terms with the same variable and power, such...