Systems of Equations & Inequalities Test Review

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 represent a system of equations graphically?

Back

Graphically, a system of equations is represented by the lines of the equations on a coordinate plane. The point(s) where the lines intersect represent the solution(s).

Front

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

Back

A consistent system has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

Front

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

Back

An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

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 a linear inequality?

Back

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region.

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 (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line divides the coordinate plane into two regions, one that satisfies the inequality and one that does not.