Systems of Non-Linear Equations 2

Front

What is a system of non-linear equations?

Back

A system of non-linear equations is a set of two or more equations where at least one of the equations is non-linear, meaning it cannot be represented as a straight line on a graph.

Tags

CCSS.HSA.REI.C.7

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the graphical representation of a non-linear equation?

Back

The graphical representation of a non-linear equation can be a curve, such as a parabola, circle, or hyperbola, rather than a straight line.

Tags

CCSS.HSA.REI.D.12

Front

How can you determine the number of solutions in a system of non-linear equations?

Back

The number of solutions can be determined by analyzing the graphs of the equations: they may intersect at zero, one, or multiple points.

Tags

CCSS.HSA.REI.C.7

Front

What is the substitution method in solving non-linear equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the elimination method in solving non-linear equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is a common type of non-linear equation?

Back

A common type of non-linear equation is a quadratic equation, which can be expressed in the form ax² + bx + c = 0.

Front

What is the significance of the solutions (x,y) in a system of equations?

Back

The solutions (x,y) represent the points of intersection of the equations on a graph, indicating the values that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

How do you verify the solution of a system of non-linear equations?

Back

To verify the solution, substitute the values of the variables back into the original equations to check if they hold true.

Tags

CCSS.HSA.REI.C.7

Front

What is a real-world application of solving non-linear equations?

Back

Real-world applications include modeling situations in physics, engineering, economics, and biology where relationships are not linear.