Non-Linear Systems

Front

What is a non-linear system?

Back

A non-linear system is a system of equations in which at least one equation is not linear, meaning it cannot be expressed in the form y = mx + b.

Front

What is the graphical method for solving non-linear systems?

Back

The graphical method involves plotting the equations on a graph and identifying the points where the curves intersect, which represent the solutions.

Front

What does it mean for a system to have multiple solutions?

Back

A system has multiple solutions when there are several points of intersection between the graphs of the equations, indicating more than one set of values that satisfy all equations.

Front

What is the significance of the intersection points in a non-linear system?

Back

The intersection points represent the solutions to the system, where the values of the variables satisfy all equations simultaneously.

Front

How can you determine if a solution is valid in a non-linear system?

Back

To determine if a solution is valid, substitute the values back into the original equations to see if they hold true.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a negative discriminant indicate?

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A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.