algebra

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i need help with these problems (either a solution or how to plug them into a graphing calculator):

1) Solve by substitution or elimination

4/x + 1/y + 2/z = 4

2/x + 3/y - 1/z = 1

1/x + 1/y + 1/z = 4

2)Solve the system of equations by substitution.

x^2 + y^2 = 25
x - y = 7

3) Solve the system of equations by substitution. Round the answer to the nearest hundredths.

9x^2 + 16y^2 = 140
x^2 - 4y^2 = 4

4)Solve by elimination:

1/x + 3/y = 7

4/x - 2/y = 1

Thanks!

  • algebra -

    1. add the 2nd and 3rd
    ----> 3/x + 4/y = 5 (#4)

    double the 2nd and add to the 1st
    ---> 8/x + 7/y = 6 (#5)

    8 times #4 --> 24/x + 32/y = 40
    3 times #5 --> 24/x + 21/y = 18
    subtract:
    11/y = 22
    11 = 22y
    y = 1/2

    sub back into either #4 or #4 to get x
    then back into 1st to get z

    2. from the second: x = y+7
    into the first: (y+7)^2 + y^2 = 25
    2y^2 + 14y + 24 = 0
    y^2 + 7y + 12 = 0
    (y+3)(y+4) = 0
    y = -3 or y = -4
    sub both of those into x = y+7 to get their corresponding x values

    3. from 2nd ---> x^2 = 4y^2 + 4
    sub into 1st, etc

    4. easier than #1
    multiply 1st by 4, then subtract the 2nd

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