Problem 42
Question
What is a system of linear equations in three variables?
Step-by-Step Solution
Verified Answer
A system of linear equations in three variables is a set of two or more equations, each of the form \(Ax + By + Cz = D\), which are solved simultaneously.
1Step 1: Definition of Linear Equation
First, need to know what a linear equation is. A linear equation is an equation of the form \(Ax + By + Cz = D\), where A, B, C, and D are constants and x, y, and z are variables.
2Step 2: Definition of a System of Equations
A system of equations is a set of two or more equations that we deal with at once. All the equations in the system are solved simultaneously.
3Step 3: Combining the Definitions
So a system of linear equations in three variables is a set of two or more linear equations, each involving the variables x, y, and z, dealt with at the same time.
Other exercises in this chapter
Problem 41
In Exercises \(29-42,\) solve each system by the method of your choice.$$ \left\\{\begin{array}{l} x^{2}+y^{2}+3 y=22 \\ 2 x+y=-1 \end{array}\right. $$
View solution Problem 41
In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to
View solution Problem 42
write the partial fraction decomposition of each rational expression. $$ \frac{3 x-5}{x^{3}-1} $$
View solution Problem 42
Graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x+y>3 \\\x+y
View solution