Flashcard Review: System of Equations

Front

What is a system of equations?

Back

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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you find the slope of a line from an equation?

Back

Rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.

Front

Back

The slope is -2.

Front

What is the solution to the system of equations if the graph shows two intersecting lines?

Back

The solution is the point of intersection of the two lines.

Front

What does it mean if two lines in a system of equations are the same?

Back

It means the system has infinite solutions.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines represented by the equations.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines: parallel lines (no solution), same line (infinite solutions), intersecting lines (one solution).

Front

What is the solution to the system of equations if the graph shows two parallel lines?

Back

No solution.