Graphing Linear Systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Front

What is the graphical representation of a solution to a system of linear equations?

Back

The solution is represented by the point where the lines intersect on a graph.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept is found by setting x = 0 in the equation and solving for y.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What does it mean for a system of equations to be independent?

Back

A system of equations is independent if it has exactly one solution.

Front

What is the difference between a dependent and an independent system of equations?

Back

A dependent system has infinitely many solutions (the lines overlap), while an independent system has exactly one solution (the lines intersect at one point).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

How can you check the solution of a system of equations graphically?

Back

You can check the solution by graphing both equations and verifying that the point of intersection is the solution.