Solving Systems using 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 equations?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

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 y = 4x - 1, how do you find the solution?

Back

Set 2x + 1 equal to 4x - 1 and solve for x, then substitute back to find y.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.

Front

How can 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.

Front

What does it mean if two equations in a system are identical?

Back

The system has infinitely many solutions, as they represent the same line.

Front

What is the graphical representation of a system of equations?

Back

The points where the graphs of the equations intersect represent the solutions.