# Solve the set of equations x - y + z = 6, x + y + z = 10 and x - y - z = 4

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Expert Answers

justaguide | Certified Educator

The following set of equations has to be solved for x, y and z:

x - y + z = 6 ...(1)

x + y + z = 10 ...(2)

x - y - z = 4 ...(3)

(1) - (3)

=> `2z = 2 => z = 1`

(2) + (3)

=> `2x = 14 => x = 7`

y = 10 - 7 - 1 = 2

**The solution to the set of equations is {7, 2, 1}**

Student Comments

tonys538 | Student

The set of equations x - y + z = 6, x + y + z = 10 and x - y - z = 4 has to be solved.

x - y + z = 6 gives x = 6 + y - z

Substituting for x in x + y + z = 10 gives 6 + y - z + y + z = 10 or 2y = 4 or y = 2.

Substituting for x in x - y - z = 4 gives 6 + y - z - y - z = 4 or -2z = -2 or z = 1

Substituting y = 2 and z = 1 in x = 6 + y - z gives x = 6 + 2 - 1 = 7

The solution of the given set of equations is x = 7, y = 2 and z = 1