Test System 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 by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

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

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) on a coordinate plane, where the intersection points represent the solutions.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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 region that satisfies the inequality.

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 they are not included (< or >).

Front

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

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

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?

Back

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