Solving Systems of Equations Graphically

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 one solution?

Back

It means the graphs of 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 graphs of 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 graphs of the equations are the same line, intersecting at every point.

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 3?

Back

(2, 5)

Front

What is the slope of the line represented by the equation y = 3x - 4?

Back

3

Front

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

Back

5

Front

How can you determine if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into each equation and checking for true statements.

Front

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

Back

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