Systems of Equations: 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 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 does it mean if a system of equations has no solution?

Back

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

Front

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

Back

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

Front

How do you determine if a solution is correct for a system of equations?

Back

Substitute the solution back into both equations to see if they hold true.

Front

What is the first step in using the substitution method?

Back

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

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you solve them using substitution?

Back

Set 2x + 3 = -x + 1 and solve for x.

Front

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

Back

(3, 0) is the solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.