Graphing 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 solution?

Back

It means there is at least one ordered pair (x, y) that satisfies all equations in the system.

Front

How can you solve a system of equations graphically?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solution, as the lines never intersect.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

Substitute the x and y values into each equation to see if they hold true.

Front

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

Back

It means the system has at least one solution.

Front

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

Back

It means the system has no solutions.