WOLFRAM|DEMONSTRATIONS PROJECT

System of Three Linear Equations with One Parameter

​
new example
show in the form A·

r
=
b
det(A) = 0
solution of det(A) = 0
case 1
condition
system
solution
case 2
condition
system
solution
case 3
condition
solution
Solve the system of equations:
2(k-3)y-kz+x-k
(k-3)y+kzk-1
kzk
1
2(k-3)
-k
0
k-3
k
0
0
k
×
-k
k-1
k
2
k
-3k0
k0∨k3
case 1. k0
x-6y0
-3y-1
True
x2∧y
1
3
x-3z-3
3z2
3z3
False
case 3. k≠0∧k≠3
x2∧y
1
3-k
∧z1
This Demonstration generates and solves a system of three linear equations in the variables
x
,
y
, and
z
with a parameter
k
. Depending on
k
, the system has infinitely many solutions, is inconsistent, or has a unique solution.