Solving Systems by Graphing and 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 by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is 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

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

How do you isolate a variable in an equation?

Back

You manipulate the equation to get the variable on one side by itself.

Front

What is the first step in solving the system 3x - y = 4 and x + 2y = 6 by substitution?

Back

Solve one of the equations for one variable, such as y in terms of x.

Front

What is the solution to the system of equations y = 2x + 5 and 2x + 2y = 4?

Back

(-1, 3)

Front

What is the solution to the system of equations 3x - y = 4 and x + 2y = 6?

Back

(2, 2)

Front

What is the easiest variable to isolate in the system 3x + 2y = 10 and x - 5y = 18?

Back

The x in the second equation.