6x − y + z = −3 4x − 3z = −13 2y + 5z = 15 Find the solutions?

Question

6x − y + z = −3
4x − 3z = −13
2y + 5z = 15
Find the solutions?

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Isabella 2 weeks 2021-10-10T18:46:55+00:00 1 Answer 0

Answers ( )

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    2021-10-10T18:48:26+00:00

    Answer:

    The solution of the equation are x = – 1 , y = 0 and z = 3

    Step-by-step explanation:

    Given three linear equation as :

    6 x – y + z = – 3        ……A

    4 x – 3 z = – 13           ……B

    2 y + 5 z = 15            ……C

    Solving eq A and C

    I.e 2× (6 x – y + z ) = -3 ×2

    or, 12 x – 2 y + 2 z = – 6

    So, ( 12 x – 2 y + 2 z ) + ( 2 y + 5 z) = – 6 + 15

    Or,  12 x + 7 z = 9         ……D

    Solving eq B and D

    I.e 3 × ( 4 x – 3 z ) = – 13 × 3

    or, 12 x – 9 z = – 39

    So, (   12 x + 7 z ) – ( 12 x – 9 z ) = 9 + 39

    or,  16 z = 48

    ∴   z = \frac{48}{16}

    i.e  z = 3

    put the value of z in eq D

    So, 12 x + 7×3 = 9  

    Or, 12 x = 9 – 21

    or,  12 x = – 12

    ∴   x = –  \frac{12}{12}

    I.e  x = – 1

    Now, Put The value of z in eq C

    or, 2 y + 5 z = 15    

    or,  2 y + 5 × 3 = 15

    Or,  2 y = 15 – 15

    or,  2 y = 0  

    ∴  y = 0

    Hence The solution of the equation are x = – 1 , y = 0 and z = 3  Answer

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