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 one solution?

Back

The two lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

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

Back

The two lines represented by the equations are the same line, overlapping each other.

Front

What is the elimination method in solving systems of equations?

Back

A method where one equation is manipulated to eliminate one variable, allowing for the other variable to be solved.

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

Solve for x and y: y = 2/3x - 2, y = -x + 3

Back

(3, 0)

Front

Solve the system of equations by elimination: -x + y = -13, -8x - 4y = -8

Back

(5, -8)

Front

Solve for x and y: 3x + 2y = 16, 7x + y = 19

Back

(2, 5)

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.