Sections 5.1-5.4 Review - Solving Linear Systems

Front

What is a linear system of equations?

Back

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

Front

What does it mean for a linear system to have a unique solution?

Back

A linear system has a unique solution if the equations intersect at exactly one point in the coordinate plane.

Front

What are the possible outcomes when solving a linear system?

Back

The possible outcomes are: one unique solution, infinitely many solutions, or no solution.

Front

How can you determine if a linear system has no solution?

Back

A linear system has no solution if the equations represent parallel lines that 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 substituting that expression into the other equation.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you graphically represent a system of linear equations?

Back

You can graphically represent a system of linear equations by plotting each equation on the same coordinate plane and observing their intersections.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and position of the line in the coordinate plane.

Front

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

Back

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