Nonlinear Systems

Front

What is a nonlinear system?

Back

A nonlinear 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 does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the equations represent parallel lines that never intersect.

Front

How do you identify the solution to a system of nonlinear equations graphically?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What is the first step in solving the system: y = x^2 + 3x - 5 and y = x + 3?

Back

Set the equations equal to each other: x^2 + 3x - 5 = x + 3.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is the graphical representation of the equation y = x^2?

Back

The graph is a parabola that opens upwards with its vertex at the origin (0,0).

Front

How can you determine if a system of equations is independent?

Back

A system is independent if it has exactly one solution, meaning the lines intersect at a single point.

Front

What is the method of substitution in solving systems of equations?

Back

The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the method of elimination in solving systems of equations?

Back

The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.