System 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 if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

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

Back

They have infinitely many solutions because they overlap completely.

Front

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

Back

They have one unique solution, which is the point of intersection.

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.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying points of intersection.

Front

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

Back

(1, 3) is the solution.

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.