Mathematics

Question

Solve for w, x, y, z

x + 2y - z = 3
2x - y + z - w = -3
y + 2z - w = -7
x + 3y + 2z + 2w = 3 ​

1 Answer

  • Answer:

    x= 1; y= 0; z= -2 and w= 3.

    Step-by-step explanation:

    Given that,

    1) x + 2y - z = 3

    2) 2x - y + z - w = -3

    3) y + 2z - w = -7

    4) x + 3y + 2z + 2w = 3 ​

    now, from 1) z = x + 2y -3 →→(5)

    from 2) w = 2x -y + z +3

             ⇒w = 2x -y + x + 2y -3 +3  (from (5))

                w = 3x + y →→(6)

    Now substitute (5) and (6) in 3), we get

    y +2(x + 2y -3) - (3x + y) = -7

    ⇒ 4y - x = -1 →→→(7)

    Now substitute (5) and (6) in 4), we get

    x + 3y + 2(x + 2y -3) + 2(3x + y) = 3

    ⇒ 9x +9y = 9

    ⇒ x + y =1 →→→(8)

    ⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1

    y = 0 and x = 1

    substituting these values in

    (5) and (6) gives, z = -2 and w = 3

    ⇒ x= 1; y= 0; z= -2 and w= 3.

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