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 a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

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

Front

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

Back

By identifying the point where the graphs of the equations 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 graphical representation of the equation y = 3?

Back

A horizontal line that crosses the y-axis at 3.

Front

What is the graphical representation of the equation x = -2?

Back

A vertical line that crosses the x-axis at -2.

Front

What does it mean for two lines to intersect at a point?

Back

It means there is one unique solution to the system of equations.

Front

If two equations are identical, what can be said about their solutions?

Back

They have infinitely many solutions.

Front

What is the slope of the line represented by the equation y = 4x + 2?

Back

The slope is 4.