Systems (graphing & substitution)

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 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 the system using substitution: x = 3y + 2, 2x - y = 4.

Back

(2, 0)

Front

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

Back

It means the 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

It means the equations represent the same line, so every point on the line is a solution.

Front

Solve the system by substitution: y = 2x + 3, 3x + 2y = 12.

Back

(2, 7)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

Solve by graphing: y = -x + 4, y = 2x - 1.

Back

(1, 3)

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

Solve the system using substitution: 2y = x + 4, y = 3x - 2.

Back

(2, 3)