How do you determine if a system is independent dependent or inconsistent?

If a consistent system has exactly one solution, it is independent .

1. If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
2. If a system has no solution, it is said to be inconsistent .

What are the steps in solving problems involving systems of linear equations in two variables by graphing?

1. Step 1: Graph the first equation.
2. Step 2: Graph the second equation on the same coordinate system as the first.
3. Step 3: Find the solution.
4. Step 4: Check the proposed ordered pair solution in BOTH equations.
5. Step 1: Graph the first equation.
6. Step 2: Graph the second equation on the same coordinate system as the first.

How many solutions does an inconsistent system of linear equations have?

no solution
A consistent system of equations has at least one solution, and an inconsistent system has no solution.

What is understanding the problem?

Understanding the problem is the first step of any problem-solving. The second step is defining how you measure success. After all, you would like to know if your solution is actually solving the problem.

How many solutions does a dependent system of linear equations have?

An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.

How can you recognize a dependent system of equations by analyzing the equations?

We can determine whether a system is dependent by graphing it, examining the equations, or using algebra. When graphed, the equations appear as one line. Examining the equations in the same format, we may see that one equation is a multiple of the other.

How do you solve problems involving systems of linear equations in two variables by substitution?

To solve systems using substitution, follow this procedure:

1. Select one equation and solve it for one of its variables.
2. In the other equation, substitute for the variable just solved.
3. Solve the new equation.
4. Substitute the value found into any equation involving both variables and solve for the other variable.

How do you solve a system of linear equations?

Solving Systems of Linear Equations. A system of linear equations is just a set of two or more linear equations. In two variables ( x and y ) , the graph of a system of two equations is a pair of lines in the plane. There are three possibilities: The lines intersect at zero points.

What is a nonlinear system of equations?

A nonlinear system of equations is a system in which at least one of the equations is not linear, i.e. has degree of two or more. Note as well that the discussion here does not cover all the possible solution methods for nonlinear systems.

How do you know if an equation is consistent or inconsistent?

A consistent system of linear equations solved by substitution will produce one solution, as described above. That solution will produce a true statement when substituted into every equation in the system. An inconsistent system of linear equations solved by substitution will produce a false statement, such as “0 = 3”.

What is the graph of a system of linear equations?

A system of linear equations is just a set of two or more linear equations. In two variables (x and y) , the graph of a system of two equations is a pair of lines in the plane. There are three possibilities: The lines intersect at zero points.