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 to graph a system of equations?

Back

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

Front

What is the solution to a system of equations?

Back

The point 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 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 rise over run.

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 linear equation?

Back

Find the y-intercept, plot it, then use the slope to find another point.

Front

What is the substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.