M3/Trig. Ch. 7 Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have a solution?

Back

A solution is an ordered pair (x, y) that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What are the three main methods to solve a system of equations?

Back

Graphing, substitution, and elimination.

Front

What is the elimination method?

Back

A method where you add or subtract equations to eliminate one variable.

Front

What is the substitution method?

Back

A method where you solve one equation for one variable and substitute that value into the other equation.

Front

What is Cramer's Rule?

Back

A mathematical theorem used to solve systems of linear equations using determinants.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

By analyzing the intersection points of the linear and quadratic graphs.