Math  /  Algebra

QuestionSolve the system of equations. x3yz=6x+8y4z=162x15y+7z=30\begin{aligned} x-3 y-z & =6 \\ -x+8 y-4 z & =-16 \\ 2 x-15 y+7 z & =30 \end{aligned}

Studdy Solution
Verify the solution by substituting x=4z x = 4z and y=z2 y = z - 2 into the third original equation:
2(4z)15(z2)+7z=302(4z) - 15(z - 2) + 7z = 30
Simplify:
8z15z+30+7z=308z - 15z + 30 + 7z = 30
Combine like terms:
0z+30=300z + 30 = 30
This equation is also always true. Therefore, the solution is valid for any z z .
The solution is a line of infinite solutions given by: x=4z,y=z2,z=z x = 4z, \quad y = z - 2, \quad z = z

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