Math  /  Algebra

Question12x12y+16z=446x+2y6z=1075x5y20z=0\begin{aligned} 12 x-12 y+16 z & =44 \\ 6 x+2 y-6 z & =-10 \\ 75 x-5 y-20 z & =0 \end{aligned}
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is x=x= \square \square , y=y= (Simplify your answer.) and z=z= \square . B. The system is dependent. There are infinitely many solutions. C. The system is inconsistent. There is no solution.

Studdy Solution
Solve for the variables using back substitution:
From the third row: 5z=5 5z = -5 z=1 z = -1
Substitute z=1 z = -1 into the second row: 8y14(1)=32 8y - 14(-1) = -32 8y+14=32 8y + 14 = -32 8y=46 8y = -46 y=468=234 y = -\frac{46}{8} = -\frac{23}{4}
Substitute y=234 y = -\frac{23}{4} and z=1 z = -1 into the first row: 12x12(234)+16(1)=44 12x - 12\left(-\frac{23}{4}\right) + 16(-1) = 44 12x+6916=44 12x + 69 - 16 = 44 12x+53=44 12x + 53 = 44 12x=9 12x = -9 x=912=34 x = -\frac{9}{12} = -\frac{3}{4}
The solution is: x=34,y=234,z=1 x = -\frac{3}{4}, \quad y = -\frac{23}{4}, \quad z = -1
The correct choice is A. There is one solution. The solution is x=34 x = -\frac{3}{4} , y=234 y = -\frac{23}{4} , z=1 z = -1 .

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord