Systems 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 no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What is the solution of a system of equations?

Back

The ordered pair that satisfies all equations in the system.

Front

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

Back

The equations represent the same line, meaning they overlap completely.

Front

How can you determine if two lines are intersecting?

Back

If the slopes of the lines are different, they will intersect at one point.

Front

What is the graphical representation of a system of equations?

Back

The points where the lines intersect represent the solutions to the system.

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 the equations y = 2x + 1 and y = 4x - 1 are graphed, what is the point of intersection?

Back

(1, 3)

Front

What is the cost equation for renting kayaks at Company A?

Back

c = 5h + 20