Systems of Equations

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 to the system is the set of values that satisfy all equations simultaneously.

Front

What does it mean if a system of equations has a unique solution?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

No solution means that there is no set of values for the variables that can satisfy all equations in the system, often due to parallel lines.

Front

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

Back

Infinitely many solutions occur when the equations represent the same line, meaning any point on the line is a solution.

Front

How can you determine if a system of equations has a unique solution, no solution, or infinitely many solutions?

Back

You can determine this by graphing the equations or using methods like substitution or elimination to analyze the relationships between the equations.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the graphs intersect.

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

How do you interpret the solution (3, -1) in the context of a system of equations?

Back

The solution (3, -1) means that when x = 3 and y = -1, both equations in the system are satisfied.