Graphing systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point(s).

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of 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 lines are the same, meaning they overlap completely.

Front

How do 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 steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

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

Back

By identifying the intersection point of the graphed lines.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for a variable and substitute it into the other equation.