Systems of Equations/Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of inequalities?

Back

The solution set is represented by a shaded region on the graph.

Front

What does the boundary line represent in a system of inequalities?

Back

It represents the values that satisfy the equation; points on the line may or may not be included in the solution set.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates they are not (> or <).

Front

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

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

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

Front

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

Back

A consistent system has at least one solution, which can be either one solution or infinitely many.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, typically represented by parallel lines.