Graphing 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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means that there are no values for the variables that can satisfy all equations in the system.

Front

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

Back

It means that there are an infinite number of values for the variables that satisfy all equations in the system.

Front

How can you graphically find the solution to a system of equations?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the slope of the line represented by the equation y = 3x - 2?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

What does the term 'consistent' mean in relation to a system of equations?

Back

A consistent system has at least one solution.

Front

What does the term 'inconsistent' mean in relation to a system of equations?

Back

An inconsistent system has no solutions.