Systems of Equations and Inequalities Review

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 no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a consistent system of equations?

Back

The lines intersect at one point.

Front

What is the graphical representation of an inconsistent system of equations?

Back

The lines are parallel and do not intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

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

Back

It means that when the coordinates of the point are substituted into the equations, they satisfy all equations.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation graphs as a straight line, while a nonlinear equation graphs as a curve.