Linear Systems Review

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What is the elimination method in solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you represent a system of equations graphically?

Back

A system of equations can be represented graphically by plotting the lines of each equation on the same coordinate plane.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the standard form of a linear equation?

Back

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

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Front

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

Back

A consistent system of equations is represented graphically by two lines that intersect at one point (one solution) or are the same line (infinitely many solutions).

Front

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

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.