Solving Systems using 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 both variables.

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 by itself, while moving all other terms to the opposite side.

Front

What is the first step in using substitution to solve a system of equations?

Back

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

Front

When using substitution, what do you do after substituting the expression into the other equation?

Back

After substituting, you solve the resulting equation for the remaining variable.

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution means that the two equations intersect at exactly one point, resulting in one set of values for the variables.

Front

What is an example of a system of equations that has no solution?

Back

An example is the system: y = 2x + 1 and y = 2x - 3, which represents two parallel lines that never intersect.

Front

What is an example of a system of equations that has infinitely many solutions?

Back

An example is the system: 2x + 4y = 8 and x + 2y = 4, where the second equation is a multiple of the first, representing the same line.

Front

How can you check your solution after solving a system of equations?

Back

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

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 both equations simultaneously.

Front

What is the general form of a linear equation in two variables?

Back

The general form is Ax + By = C, where A, B, and C are constants.