System of Equations

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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

How can you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they 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

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are equal.

Front

If two lines are perpendicular, what can be said about their slopes?

Back

The slopes of perpendicular lines are negative reciprocals of each other.

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.