Systems Of Equations by Graphing

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 two lines to intersect?

Back

It means they have a common solution, which is the point where they meet on a graph.

Front

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

Back

By plotting both equations on the same graph and identifying the point of intersection.

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

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

Back

It means there is no solution, as the lines never intersect.

Front

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

Back

No solution.

Front

What is the y-intercept of the equation y = 4 - x?

Back

4, which is the point where the line crosses the y-axis.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

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

Back

(2, 4)

Front

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

Back

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