Solving Systems of Equations by Substitution

Flashcards for solving systems of equations by substitution.

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

An algebraic method that replaces a variable in one equation with an equivalent expression from another equation to solve for the variables in the system.

Why is substitution helpful compared to graphing?

Substitution can provide an exact solution, especially when the intersection point on a graph is not easily determined (e.g., between grid lines).

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

Solve one of the equations for one variable (get the variable alone on one side of the equation).

After solving for one variable, what is the next step?

Substitute the expression found in the first step into the other equation to solve for the remaining variable.

After finding the value of one variable, what do you do?

Substitute the found value back into either of the original equations to solve for the other variable.

How many solutions does a system of equation where both equations are equal to each other has?

Infinite solutions.

When should you consider rewriting equations when solving by substitution?

When neither equation is in the form y = or x =. Solve for the variable that seems easiest to isolate.

What does it mean if, after substitution, you encounter a true statement with no variables?

The system has infinitely many solutions, indicating the two equations represent the same line.

What does it mean if, after substitution, you encounter a false statement with no variables?

The system has no solution, indicating the two equations represent parallel lines that never intersect.

When might elimination be a better approach than substitution?

When both equations have x and y on the same side with a constant on the other side, making it cumbersome to isolate a single variable.