Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a solution?

Back

It means there is at least one ordered pair (x, y) that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

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

Front

What does it mean if two lines intersect on a graph?

Back

The system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

The system of equations has no solution.

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

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What is the solution to the system: 6x + y = -1 and y = -3x - 4?

Back

(1, -7)