Systems of Equations Review

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 the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so any point on that line is a solution.

Front

How do you graph a system of equations?

Back

You graph each equation on the same coordinate plane and look for points of intersection.

Front

What is the substitution method for solving systems of equations?

Back

It involves 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

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the point of intersection in a system of equations?

Back

It is the point where the graphs of the equations meet, representing the solution to the system.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the graphical representation of the equation y = mx + b?

Back

It represents a straight line where m is the slope and b is the y-intercept.