Solving Systems by 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 substitution in the context of solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How can you determine if a system of equations has one solution, no solution, or infinite solutions?

Back

By analyzing the graphs of the equations: one solution (intersecting lines), no solution (parallel lines), infinite solutions (same line).

Front

What is the first step in solving a system of equations by substitution?

Back

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

Front

Given the equations y = 2x + 1 and x + y = 5, what is the solution?

Back

(2, 5)

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

They represent different lines and have exactly one solution.

Front

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

Back

(1, 5)

Front

How do you check if your solution to a system of equations is correct?

Back

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