Review: 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

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

Back

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

Front

How do you graph a linear equation?

Back

To graph a linear equation, convert it to slope-intercept form (y = mx + b), identify the slope (m) and y-intercept (b), and plot the line using these points.

Front

What is the slope-intercept form of a linear equation?

Back

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 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 to find the other variable.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality shows a region of the coordinate plane that satisfies the inequality, often shaded to indicate all possible solutions.

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, meaning the lines intersect at one or more points.

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What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution (intersecting lines), while an inconsistent system has no solutions (parallel lines that never intersect).

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the graphs: one solution (intersecting lines), infinitely many solutions (same line), or no solution (parallel lines).