Solving Systems (Graphing & Substitution)

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphing method for solving systems of equations?

Back

A method that involves graphing each equation on the same set of axes and identifying the point(s) where they intersect.

Front

What is the substitution method for 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 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 infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

Solve the system: y = 2x + 3 and y = -x + 1.

Back

(1, 5) is the solution.

Front

Solve the system: 2x + 3y = 6 and x - y = 2.

Back

(3, 0) is the solution.

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other.