AFDA Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is the substitution method in solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of the solution (1, -1)?

Back

The point where x=1 and y=-1 intersects on the graph.

Front

If a system of equations has the same slope but different y-intercepts, what can be concluded?

Back

The system has no solution because the lines are parallel.

Front

What is the general form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.