Solving Linear Systems & Inequalities

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 are the two main methods for solving linear systems?

Back

The two main methods for solving linear systems are elimination and substitution.

Front

What does it mean 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 graphical representation of a solution to a linear equation?

Back

The graphical representation of a solution to a linear equation is the point where the line intersects the coordinate plane.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region in a graph of inequalities represents all the possible solutions that satisfy the inequality.

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 difference between a consistent and an inconsistent system?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the substitution method for solving linear equations?

Back

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

Front

What is the elimination method for solving linear equations?

Back

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