How to solve Linear Equation in three variables????
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How to solve Linear Equation in three variables????
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4x - 3y + z = - 10 (i)
2x + y + 3z = 0 (ii)
- x + 2y - 5z = 17 (iii)
Pick two pairs:
4x - 3y + z = - 10
2x + y + 3z = 0
Eliminate the same variable from each system:
4x - 3y + z = - 10
2x + y + 3z = 0
4x - 3y + z = - 10
-4x - 2y - 6z = 0
-5y - 5z = - 10
2x + y + 3z = 0
- x + 2y - 5z = 17
2x + y + 3z = 0
-2x + 4y - 10z = 34
5y - 7z = 34
Solve the system of the two new equations:
-5y - 5z = - 10
5y - 7z = 34
-12z = 24
Thus,
z = - 2
substitute the value,
-5y - 5(- 2) = - 10
-5y = - 20
Thus,
y = 4
Substitute into one of the original equations:
- x + 2y - 5z = 17
- x + 2(4) - 5(- 2) = 17
- x + 18 = 17
- x = - 1
x = 1