Solving Systems 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 for a system of equations to have a unique solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines represented by the equations coincide, or are the same line.

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, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

Front

What is the solution to the system of equations 2x - y = 4 and y = -2x + 8?

Back

(3, 0)

Front

What does the graph of parallel lines indicate about a system of equations?

Back

It indicates that the system has no solution.

Front

What is the inequality represented by the graph that shows all values less than -1?

Back

x < -1