Systems of Equations - Identifying solutions

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

How can you identify the solution of a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.

Front

What is an ordered pair?

Back

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

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

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 that line is a solution.

Front

How do you solve a system of equations using substitution?

Back

You 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

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

Front

What is the graphical representation of the solution (2,4)?

Back

It is the point where x=2 and y=4 on the coordinate plane.

Front

What is the solution of the system of equations represented by the lines y=2x and y=4?

Back

The solution is (2,4), where the two lines intersect.