System of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is a solution to a system of equations?

Back

A point (x, y) that makes all equations in the system true.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has infinitely many solutions?

Back

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

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all, it is a solution.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.