Systems of Equations and Inequalities by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have an infinite number of solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the solution of a linear system?

Back

The point where the graphs of the equations intersect.

Front

What is a system of inequalities?

Back

A set of two or more inequalities that are solved together.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them with a straight line.

Front

What is slope-intercept form?

Back

A way of writing linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line from two points?

Back

By using the formula (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a graph?

Back

The point where the line crosses the y-axis.

Front

What is the difference between a solution and a feasible solution in a system of inequalities?

Back

A solution satisfies all equations, while a feasible solution satisfies all inequalities.

Front

How can you determine if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into the equations and checking if they hold true.