Question 502971: Please help me solve this.
Is this system dependent or independent?
x + 2y + z = 4
3x - 4y + z = 4
6x - 8y + 2z = 8
Answer by jrb1965(16)   (Show Source):
You can put this solution on YOUR website! You have 3 unknowns, but since the second and third equations are the same information (equation 3 is just equation 2 multiplied by 2) you will not have a unique solution so the system will be dependent.
3x - 4y +z = 4
x + 2y + z = 4
_______________ Subtracting equation 1 from equation 2
2x - 6y = 0, so x = 3y
Substituting this into equation 3
18y - 8y + 2z = 8
10y + 2z = 8, so y = 0.8 - 0.2z, and x = 3y = 2.4 - 0.6z
Substitute the x and y in terms of z into any of the equations will result in an identity equation
(2.4 - 0.6z) + 2(0.8 - 0.2z) + z = 4 (substituted into equation 1)
(2.4 - 0.6z) + (1.6 - 0.4z) + z = 4
4 = 4, true for all values of z
So this is a dependent system
x = 2.4 - 0.6z
y = 0.8 - 0.2z
for any chosen value of z
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