Systems of equations and inequalities

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation of a system of inequalities is the shaded region where all inequalities overlap.

Front

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

Back

To determine if a point is a solution, substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.

Front

What is the difference between consistent and inconsistent systems?

Back

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

Front

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

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the appropriate region based on the inequality sign.

Front

What is the role of the boundary line in a system of inequalities?

Back

The boundary line separates the shaded region (solutions) from the non-shaded region (non-solutions). It is solid for ≤ or ≥ and dashed for < or >.