Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means that there are no values for the variables that can satisfy all equations in the system, often represented by parallel lines.

Front

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

Back

It means that there are an infinite number of values for the variables that satisfy all equations, often represented by the same line.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

Front

What is the solution to the system: 5x + y = 22 and 2x - y = 6?

Back

(4, 2)

Front

What is the solution to the system: 2x + y = -1 and -4x + 6y = 42?

Back

(-3, 5), x = -3 and y = 5.

Front

How do you determine if a system of equations has no solution graphically?

Back

If the lines representing the equations are parallel, they will never intersect, indicating no solution.