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 the variables.

Front

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

Back

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

Front

How do you determine if a system of equations has one solution?

Back

A system has one solution if the lines represented by the equations intersect at exactly one point.

Front

What is the first step in using substitution to solve the system: 3x + 3y = 3 and y = 3x + 5?

Back

The first step is to substitute the expression for y from the second equation into the first equation.

Front

What is the solution to the system of equations 2x + 3y = 4 and y = 5x - 27?

Back

The solution is (5, -2).

Front

What does it mean if two lines are parallel in the context of systems of equations?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, resulting in no solutions for the system.

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 the original equations to see if they hold true.

Front

What is the significance of isolating a variable in one of the equations?

Back

Isolating a variable allows you to express it in terms of the other variable, making it easier to substitute into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the points of intersection represent the solutions to the system.

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.