Systems of Equations - Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

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 is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

How do you find the solution to a system of equations graphically?

Back

By identifying the point(s) where the graphs of the equations intersect.

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 does it mean for a system of equations to be consistent?

Back

A system that has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system that has no solutions.

Front

What is the solution to the system of equations y = 1/4x - 4 and y = -1/2x - 1?

Back

(4, 3)

Front

What is the solution to the system of equations y = -5/3x - 2 and y = 1/3x + 4?

Back

(6, 3)