Systems of Equations: Substitution Method

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

Given the equations y = 2x - 11 and 2x - 8y = 4, what is the solution using substitution?

Back

The solution is (6, 1).

Front

If you have the equations x + y = 19 and y = 3x - 1, what is the solution?

Back

The solution is (5, 14).

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.