Solve Systems by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the variables.

Front

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

Back

Make sure at least one equation is solved for one variable.

Front

When is the substitution method most effective?

Back

The substitution method is most effective when one of the equations is already solved for a variable.

Front

What does the equation 3x + 2y = 315 represent in a real-world context?

Back

It represents a situation where a person can perform a combination of tasks (like haircuts and hair dyes) within a certain time limit.

Front

How do you substitute a variable in an equation?

Back

To substitute a variable, replace the variable in the equation with the expression that equals it from another equation.

Front

What is the result of substituting y = 2x + 5 into the equation 3x - y = 7?

Back

3x - (2x + 5) = 7.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

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

Back

It means that the equations represent the same line and have infinitely many solutions.

Front

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

Back

It means that the equations represent different lines and have exactly one solution.

Front

What is the graphical interpretation of a solution to a system of equations?

Back

The solution is the point where the graphs of the equations intersect.