Graphing Linear Systems

Front

What does it mean for a system of equations to be 'Consistent and Dependent'?

Back

A system of equations is 'Consistent and Dependent' when there are infinitely many solutions, meaning the equations represent the same line.

Front

What does it mean for a system of equations to be 'Consistent and Independent'?

Back

A system of equations is 'Consistent and Independent' when there is exactly one solution, meaning the lines intersect at a single point.

Front

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

Back

A system of equations is 'Inconsistent' when there are no solutions, meaning the lines are parallel and never intersect.

Front

How do you determine the solution to a system of equations graphically?

Back

The solution to a system of equations can be found at the point where the graphs of the equations intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the solution to the system of equations: 3x + 2y = 6 and x - y = 1?

Back

(2, 0)

Front

What is the solution to the system of equations: y = 3x - 2 and y = -2x + 4?

Back

(1, 1)

Front

What is the solution to the system of equations: 2x + y = 5 and x - y = 1?

Back

(2, 1)

Front

What is the graphical representation of a consistent system of equations?

Back

The graphical representation shows two lines that intersect at one point.

Front

What is the graphical representation of a dependent system of equations?

Back

The graphical representation shows two lines that lie on top of each other, representing the same line.