System of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to find a solution by graphing?

Back

It means to find the point where two lines intersect on a graph.

Front

What is the solution to a system of equations?

Back

The ordered pair (x, y) that satisfies all equations in the system.

Front

What happens when two equations have the same slope but different y-intercepts?

Back

They are parallel and have no solution.

Front

What is an ordered pair?

Back

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

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the values of the ordered pair into each equation to see if they hold true.

Front

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

Back

It means the equations represent the same line, and every point on the line is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines representing the equations on a coordinate grid.

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

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable.