Application of Systems

Front

What does it mean if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and do not intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

How do you determine if two lines are parallel when given their equations?

Back

If the slopes of the two lines are equal and the y-intercepts are different, the lines are parallel.

Front

What is the general form of a linear equation in two variables?

Back

Ax + By = C, where A, B, and C are constants.

Front

How can you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) of intersection.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations and manipulate them to eliminate one variable by addition or subtraction.

Front

If x + y = 14 and x - y = 8, what are the values of x and y?

Back

x = 11 and y = 3.

Front

What is the significance of the coefficients in a system of linear equations?

Back

They represent the relationship between the variables in the equations.