math

posted by .

solve the system of equations in three variables
-3x+y-z=-10

  • math -

    We need two more equations.

  • math -

    -3x+y-z=-10
    -4x+2y+3z=-1
    2x+3y-2z=-5

    sorry.

  • math -

    Your goal is to take these 3 equations in 3 variables down to 2 equations in 2 variables then the problem becomes much easier.

    you have to decide which variable to eliminate first and you have to do this twice.

    Looking at the problem. I might try to eliminate the y's

    I will take -2 times the first equation and add it to the second equation.

    6x -2y + 2z = 20
    -4x +2y +3z = -1

    This reduces to 2x + 5z = 19 Save this equation..

    Now, I have to use the 3rd equation

    2x + 3y -2z = 5

    It is easier for me to eliminate the 3y if I use the first equation again.

    I multiply the first equation by -3

    2x + 3y -2z = -5
    9x -3y+3z =30

    add these two: 11x + z = 25

    Now, go to the problem you saved

    2x + 5z = 19
    11x + z = 25

    Multiply the second equation by -5 and that will help you eliminat the z's. solve for x.

    Take your answer for x and subsitute into one of these two equations to find z.

    Take your answers for x and z and substitute these values into one of the original equations to find y.

    Once you have x, y, z... check all 3 in each of the three equations to make sure you haven't made a mistake.

    It is really, really easy to make a mistake with these equations. If you get lost. Just start over try eliminating a different variable. Sometimes that helps.

  • math -

    y = 3x+z-10
    substituting values from the first into the others,

    -4x+2(3x+z-10)+3z = -1
    2x+3(3x+z-10)-2z = -5
    or
    2x+5z = 19
    11x+z = 25

    Now, z=25-11x, so

    2x + 5(25-11x) = 19
    -53x = -106
    x = 2
    z = 25-11x = 3
    y = 3x+z-10 = -1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. to annonymus can you help me with math

    How do i solve inequalitites with three variables. I still can't figure it outplease help. x+y=1 y-z=-3 2x+3y+z=1 the answers are 3,-2,1 how do get there by solving linear equations with three variables. 5x-2y-z=2 -y+2z=11 x+y+z=-3
  2. math

    How do you solve system of equations and tell if they're consistant and independant,consistant and dependent,and inconsistant?
  3. Algebra question

    When you solve a system of equations by the substitution method, how do you determine whether the system of equations is dependent?
  4. Algebra 2

    1.) Write a system of equations that has NO solution. 2.) If you wanted to eliminate the y variables in the system of equations below, what would you multiply the first and second equations by?
  5. Algebra 2

    1.) Write a system of equations that has NO solution. 2.) If you wanted to eliminate the y variables in the system of equations below, what would you multiply the first and second equations by?
  6. Algebra 2

    1.) Write a system of equations that has NO solution. 2.) If you wanted to eliminate the y variables in the system of equations below, what would you multiply the first and second equations by?
  7. algebra 2

    how do u solve a system of linear equations in three variables?
  8. Algebra 2

    What would be the simplest way to eliminate one of the variables?
  9. Alg 2

    Today we learned how to solve systems of equations with 3 variables, however my teacher didn't go over how to do a problem where not every single equation in the system has the 3 variables. Can someone point me to a place that explains …
  10. Algebra

    the sum of two numbers is 18. The difference between three times the lesser number and the greater number is 10. A)define variables and formulate a system of equations from this situation B)solve your system of equations algebraically …

More Similar Questions