Solving Systems 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 the graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Front

How do you find the solution to the system y = 5x + 1 and y = 3x + 13?

Back

Set the equations equal to each other: 5x + 1 = 3x + 13, solve for x, then substitute back to find y. Solution: (6, 31).

Front

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

Back

Substituting y from the first equation into the second gives the solution: (0, 5).