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System of Linear Equation in Three Variables

Concept:

As a linear equation ax+by=c in two variables x and y can be represented by a line in a two-dimensional rectangular coordinate system, so can a linear equation ax+by+cz=d in three variables x, y, and z be represented by a plane in a three-dimensional rectangular coordinate system. And as two non-parallel lines intersect at a point, so can three mutually non-parallel planes intersect at a point.

Eqn 1
x +
y +
z =
 a12:
 a13:
  c1:
Eqn 2
x +
y +
z =
 a22:
 a23:
  c2:
Eqn 3
x +
y +
z =
 a32:
 a33:
  c3:
(no solution )
Show intersection of Eqns

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

1. What is the solution of the system 9 x + 3 y - 2 z = 73 4 x - 7 y - 5 z = 79 - x + 6 y + 8 z = 17 ?
2. Solve 5.72 x - 7.64 y + 3.08 z = 35.828 0.551 x + 1.023 y + 0.259 z = 1.8079 45.1 x + 22.7 y - 51.5 z = 86.59
3. Find the values of x, y, and z for which 4 x + 9 z = 3 y + 10 7 y + z = 2 x - 82 5 x = 6 z + 65 .
4. 0 . 428 , - 0 . 306 , 0 . 91 is a solution to which system of equations?

n be any number from to

t can be any number from to