Question
Find the values of x, y and z, so as to satisfy the
equations given below: x + y + z = 12; x + y – z = 6; x – y + z = 4Solution
We are given: x + y + z = 12 x + y − z = 6 x − y + z = 4 Add (1) and (2): (x + y + z) + (x + y − z) = 12 + 6 ⇒ 2x + 2 y = 18 ⇒ x + y = 9 Subtract (2) from (1): (x + y + z) − (x + y − z) = 12 − 6 ⇒ 2z = 6 ⇒ z = 3 Substitute z = 3 into (3): x − y + 3 = 4 ⇒ x − y = 1 Now, solve: x + y = 9 x − y = 1 Add both: 2x = 10 ⇒ x = 5 Then, y = 4
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