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 system of equations to have one solution?

Back

A system has one solution when the graphs of the equations intersect at exactly one point.

Front

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

Back

A system has no solution when the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system has infinite solutions when the equations represent the same line, meaning they intersect at every point on that line.

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

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is non-negative.

Front

How can you determine the number of solutions from a graph?

Back

Count the number of intersection points of the lines: one point means one solution, no points means no solution, and overlapping lines mean infinite solutions.