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 a system of equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations true.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean when two lines intersect on a graph?

Back

It means that the system of equations has a unique solution at the point of intersection.

Front

What is the meaning of 'no solution' in a system of equations?

Back

It means the lines are parallel and never intersect.

Front

What is the meaning of 'infinitely many solutions' in a system of equations?

Back

It means the lines coincide, representing the same line.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope of a line from its equation?

Back

The slope is the coefficient of x in the slope-intercept form.

Front

What is the y-intercept of a line?

Back

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