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Solve for x, y , and z in terms of a, b , and c . {-x+y+z =a {x-y+z=b {x+y-z=c

User Comonad
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Final answer:

To solve the system of equations for x, y, and z, you add and subtract the given equations to isolate and solve for each variable sequentially, resulting in x = (b + c) / 2, y = (a + c) / 2, and z = (a + b) / 2.

Step-by-step explanation:

To solve for x, y, and z in terms of a, b, and c, we have the system of equations:


  • -x + y + z = a

  • x - y + z = b

  • x + y - z = c

Add the first and second equations to eliminate y:


  • -x + y + z + x - y + z = a + b

  • 2z = a + b

  • z = (a + b) / 2

Substitute the value of z into the third equation:


  • x + y - (a + b) / 2 = c

  • x + y = c + (a + b) / 2

Now we can add the first and third equations to eliminate z:


  • -x + y + z + x + y - z = a + c

  • 2y = a + c

  • y = (a + c) / 2

Finally, solve for x by substituting the values of y and z into the second or first equation:


  • x - (a + c) / 2 + (a + b) / 2 = b

  • x = b + (a + c) / 2 - (a + b) / 2

  • x = (b + c) / 2

In summary, the solution is:


  • x = (b + c) / 2

  • y = (a + c) / 2

  • z = (a + b) / 2

User Xiaofan
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