Solve for x, y and z, given the following equations: x + y + z = 6 2x - y + 3z = 9 -x + 2y + 2z = 9

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to solve for x, y and z using

x + y + z = 6 … (1)

2x –y + 3z = 9 … (2)

-x + 2y + 2z = 9 … (3)

Add (1) and (3)

=> 3y + 3z = 15

=> y + z = 5

Substitute this in (1)

=> x + 5 = 6

=> x = 1

substitute this in (2)

=> 2 – y + 3z = 9

=> 2 – (5 – z) + 3z = 9

=> 2 – 5 + z + 3z = 9

=> -3 + 4z = 9

=> 4z = 12

=> z = 3

y + z = 5

=> y = 5 – 3

=> y = 2

Therefore x = 1, y = 2 and z = 3.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial