linear equations in three ariables example
Answers
Answer:
In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables
(
x
,
y
,
z
)
,
(x,y,z), is called an ordered triple.
To find a solution, we can perform the following operations:
Interchange the order of any two equations.
Multiply both sides of an equation by a nonzero constant.
Add a nonzero multiple of one equation to another equation.
Graphically, the ordered triple defines the point that is the intersection of three planes in space. You can visualize such an intersection by imagining any corner in a rectangular room. A corner is defined by three planes: two adjoining walls and the floor (or ceiling). Any point where two walls and the floor meet represents the intersection of three planes.
A GENERAL NOTE: NUMBER OF POSSIBLE SOLUTIONS
The planes illustrate possible solution scenarios for three-by-three systems.
Systems that have a single solution are those which, after elimination, result in a solution set consisting of an ordered triple
{
(
x
,
y
,
z
)
}
{(x,y,z)}. Graphically, the ordered triple defines a point that is the intersection of three planes in space.
Systems that have an infinite number of solutions are those which, after elimination, result in an expression that is always true, such as
0
=
0
0=0. Graphically, an infinite number of solutions represents a line or coincident plane that serves as the intersection of three planes in space.
Systems that have no solution are those that, after elimination, result in a statement that is a contradiction, such as
3
=
0
3=0. Graphically, a system with no solution is represented by three planes with no point in common.
Answer:
ax+ by+cz +d = 0
Step-by-step explanation:
3x+4y-7z-2=0