Solving Systems with 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

What is the first step in solving a system using substitution?

Back

Isolate one variable in one of the equations.

Front

How do you determine the number of solutions in a system of equations?

Back

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

Front

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

Back

(2, 0) - found by substituting y into the first equation.

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: x + y = 5 and y = 3?

Back

(2, 3) - substitute y = 3 into the first equation.

Front

What is the solution to the system: x = 4 and y = 2x + 1?

Back

(4, 9) - substitute x = 4 into the second equation.