Get 9 7 Solving Linear Nonlinear Systems Answers

There are three possible types of solutions to a system of equations representing a line and a parabola: (1) no solution, the line does not intersect the parabola; (2) one solution, the line is tangent to the parabola; and (3) two solutions, the line intersects the parabola in two points.

An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation. For example \[3x^{2}\] + 2x + 1 = 0, 3x + 4y = 5, this is the example of nonlinear equations, because equation 1 has the highest degree of 2 and the second equation has variables x and y.

A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.

Key Concepts. There are three possible types of solutions to a system of equations representing a line and a parabola: (1) no solution, the line does not intersect the parabola; (2) one solution, the line is tangent to the parabola; and (3) two solutions, the line intersects the parabola in two points.

The point (5,3) means x = 5 and y = 3 pair up together. Replace x and y with 5 and 3 in that order for each equation. We get a false statement at the end, so the given point is not a solution to the system. Both equations must be true at the same time in order to get a solution.

Step 1: Simplify if needed. ... Step 2: Solve one equation for either variable. ... Step 3: Substitute what you get for step 2 into the other equation. ... Step 4: Solve for the remaining variable. ... Step 5: Solve for second variable. Step 6: Check the proposed ordered pair solution(s) in BOTH original equations.

These methods include the substitution method and the elimination method. Other algebraic methods that can be executed include the quadratic formula and factorization.