Math 1: CW 5.1 Systems of equations 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 on a graph?

Back

It means that the two equations have a common solution (x, y) at the point of intersection.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

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

Front

How can you determine the number of solutions in a system of equations?

Back

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

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and look for points of intersection.

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts, resulting in no solutions.