Systems of Equations (All three methods)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines represented by the equations are parallel and never 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 if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning they intersect at every point on that line.

Front

How do you graphically represent a system of equations?

Back

By plotting the equations on the same coordinate plane and observing where they intersect.

Front

What is the graphical interpretation of intersecting lines in a system of equations?

Back

The point of intersection represents the solution to the system.

Front

How can you check the solution of a system of equations?

Back

By substituting the solution back into the original equations to see if they hold true.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.