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 if two lines are parallel in a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

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

Back

It means there are infinitely many solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

It means there is exactly one solution to the system, which is the point of intersection.

Front

How do you solve a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

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

Back

(1, 3)

Front

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

Back

(1, 1)

Front

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

Back

It means the lines are parallel and do not intersect.

Front

What is the graphical representation of the equation y = 3x + 2?

Back

A straight line with a slope of 3 and a y-intercept of 2.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the two equations represent the same line, they have infinitely many solutions.