Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

solve the following linear equations ?

x- 2y + 3z = 7

2x + y + z = 4

-3x + 2y - 2z = -10

9 Answers

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  • 3 weeks ago

    2y - 2z = -10+3x, y + z = 4 - 2x, x = 7 + 2y - 3z

    y(x) = ( (-10+3x)×1+2×(4 - 2x) ) / (2×1+2×1) = -(x + 2)/4z(x) = ( 2×(4 - 2x) - (-10+3x)×1) / (2×1+2×1) = (-7x + 18)/4

    x = 7 + 2y - 3z = 7 + 2(-(x + 2)/4) - 3(-7x + 18)/4 = (19 x - 30)/4 = 2

    y = -(2 + 2)/4 = -1

    z = (-7×2 + 18)/4 = 1

    Solution: (2, -1, 1)

  • 1 month ago

    x-2y+3z=7-------(1)

    2x+y+z=4--------(2)

    -3x+2y-2z=-10--(3)

    =>

    x=2

    y=-1

    z=1

    directly from my own software.

    Handy solution:

    (1)+(3)=>

    -2x+z=-3------(4)

    -2(2)+(3)=>

    7x+4z=18----(5)

    -4(4)+(5)=>

    15x=30

    =>

    x=2

    z=1 from (4)

    y=4-4-1=-1 from (2)

  • 1 month ago

    {z = -x/3 + (2 y)/3 + 7/3, z = -2 x - y + 4, z = -(3 x)/2 + y + 5}

    x = 2,  y = -1,  z = 1

  • 1 month ago

    x - 2y + 3z = 7 

    2x + y + z = 4

    -3x + 2y - 2z = -10

    5x + 5z = 15

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  • 1 month ago

    If we have three equations in three unknowns, we need to combine them to get two equations in two unknowns.

    2(2) + (1) => 5x + 5z = 15

    i.e. x + z = 3...(4)

    2(2) - (3) => 7x + 4z = 18...(5)

    (4) into (5) for x gives:

    7x + 4(3 - x) = 18

    so, 3x + 12 = 18

    Hence, x = 2

    Then, z = 1 => y = -1

    Therefore, (x, y, z) => (2, -1, 1)

    :)>

  • 1 month ago

    x- 2y + 3z = 7  ............................. (1)

    2x + y + z = 4   ..............................(2)

    -3x + 2y - 2z = -10  .......................(3)

    From (1) :  x  =  2 y - 3 z + 7 .............................. (a)

    Substitute this value one by one in eqns (2) and (3)  and siplify -

    =>  2 (2 y - 3 z + 7) + y + z  =  4      ...   from (2)

    => 5 y - 5 z  =  - 10  

    =>  y - z  =  - 2    ................................ (3)

    Again from (3) we get -

    =>  - 3 (2 y - 3 z + 7) + 2 y - 2 z  =  - 10 

    =>  - 4 y + 7 z  =   11   .............. (4)

    Now solving simultaneous eqns (3) and (4) :

    y  =  - 1 and z  =  + 1

    Substituting these values in (a) above :

    x  =  2 ( - 1 ) - 3 ( 1 )  +  7

    =>  x  =  - 2 - 3 + 7  =  2

    ================================

    Answer :  x  =  + 2,  y  =  - 1  and z = + 1 

    \================================

     

  • 1 month ago

    Double equation 2:

    4x + 2y + 2z = 8

    Add that to equation 1:

    5x + 5z = 15

    Divide that by 5:

    x + z = 3, so z = 3 - x

    Add equations 1 and 3:

    -2x + z = -3

    Substitute z = 3 - x into that:

    -2x + 3 - x = -3

    -3x = -3 - 3

    -3x = -6

    x = (-6)/(-3) = 2

    Substitute that into z = 3 - x:

    z = 3 - 2 = 1

    Substitute x and z into equation 2:

    2*2 + y + 1 = 4

    4 + y + 1 = 4

    y = 4 - 4 - 1

    y = -1

  • 1 month ago

    I agree with anonymous.

    mathway helps with math

    x=2

    y=-1

    z=1

  • Anonymous
    1 month ago

    mathway.com. stupid

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