Mathematics
Precalculus. I am not that good at it

### Question Description

I’m studying for my Calculus class and need an explanation.

• Write a problem for a classmate to solve that can be translated to a system of two (2) or more equations in at least two (2) variables. Explain your answer.

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If a system of linear equations has at least one solution, it is consistent. If the system has no solutions, it is inconsistent. If the system has an infinity number of solutions, it isdependent. Otherwise it is independent.

A linear equation in three variables describes a plane and is an equation equivalent to the equation

where A, B, C, and D are real numbers and A, B, C, and D are not all 0.

Example 2:

Let's create three equations from the given points.

We are going to show you how to solve this system of equations three different ways:

1) Substitution, 2) Elimination 3) Matrices

SUBSTITUTION:

The process of substitution involves several steps:

Step 1: Solve for one of the variables in one of the equations. It makes no difference which equation and which variable you choose. Let's solve for [img width="17" height="15" align="BOTTOM" border="0" src="http://www.sosmath.com/soe/SE3001/img21.gif" alt="$C$"> in equation (1).

Step 2: Substitute this value for [img width="17" height="15" align="BOTTOM" border="0" src="http://www.sosmath.com/soe/SE3001/img21.gif" alt="$C$" > in equations (2) and (3). This will change equations (2) and (3) to equations in the two variables  and . Call the changed equations (4) and (5), respectively.

 (4) (5)

Step 3: Solve for [img width="16" height="14" align="BOTTOM" border="0" src="http://www.sosmath.com/soe/SE3001/img23.gif" alt="$A$" > in equation (4).

Step 4: Substitute this value of  in equation (5). This will give you an equation in one variable.

Step 5:  Solve for .

Step 6: Substitute this value of  in equation (4) and solve for

Step 7: Substitute  for  and  for  in equation (1) and solve for .

The solution: The equation of the circle that contains the points , and  is

Step 8: Check the solutions:

ELIMINATION:

The process of elimination involves several steps: First you reduce three equations to two equations with two variables, and then to one equation with one variable.

Step 1: Decide which variable you will eliminate. It makes no difference which one you choose. Let us eliminate  first..

Step 2: Add equations (1) and (2) to form equation (4), then add equations (2) and (3) to form equation (5). Equations (4) and (5) will contain the variables A and B.

Step 3: We now have two equations with two variables. Let's simplify these two equations.

Step 4: Add the simplified equations (4) and (5) to create equation (6) with just one variable.
Step 5: Solve for [img width="16" height="14" align="BOTTOM" border="0" src="http://www.sosmath.com/soe/SE3001/img23.gif" alt="$A$" > in equation (6).

Step 6: Substitute  for  in equation (4) and solve for B.

Step 7: Substitute  for  and  for  in equation (1) and solve for .

MATRICES:

Step 1: Create a three-row by four-column matrix using coefficients and the constant of each equation.

We want to convert the original matrix

to the equivalent matrix.

Step 2: We work with column 1 first. We want a 1 in Cell 11 [Row 1-Col 1]. To achieve this, multiply Row 1 by  to form a new Row 1.

Step 3: Add -2 times Row 1 to Row 2 to form a new Row 2, and add -6 times Row 1 to Row 3 to form a new Row 3.

Step 6: Let's now manipulate the matrix so that there is a 1 in Cell 33. We do this by multiplying Row 3 by

Step 7: Let's now manipulate the matrix so that there are zeros in Cells 13 and 12.

Iland A (747)
Boston College
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Review

Anonymous
Thanks for the help.

Anonymous
Outstanding. Studypool always delivers quality work.

Anonymous
Tutor was very helpful and took the time to explain concepts to me. Very responsive, managed to get replies within the hour.

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