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Math Help - Simultaneous Equation I

  1. #1
    Member
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    Jun 2009
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    Simultaneous Equation I

    Help me to solve this please?

    1. 2^2+xy-2y^2=-2
    x^2-3xy-5y^2=5

    2. \frac{x+2y-1}{3}=\frac{2x-y+7}{4}=\frac{3x+2y-3}{5}=z
    Find x, y, z.

    3. x^3-y^3=35
    x-y=5

    Answer:
    1. x=\pm5, y=\mp4

    2. x=4, y=3, z=3

    3. x=3, y=-2; x=2, y=-3
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  2. #2
    Super Member
    Joined
    May 2009
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    527
    Is there a typo in #1?

    Quote Originally Posted by cloud5 View Post
    3. x^3-y^3=35
    x-y=5
    Solve by substitution.
    \begin{aligned}<br />
x - y &= 5 \\<br />
x &= y + 5 \\<br />
x^3 - y^3 &= 35 \\<br />
(y + 5)^3 - y^3 &= 35 \\<br />
y^3 + 15y^2 + 75y + 125 - y^3 &= 35 \\<br />
15y^2 + 75y + 125 &= 35 \\<br />
15y^2 + 75y + 90 &= 0 \\<br />
15(y^2 + 5y + 6) &= 0 \\<br />
15(y + 2)(y + 3) & = 0<br />
\end{aligned}

    \begin{aligned}<br />
y + 2 &= 0 \\<br />
y &= -2 \\<br />
x &= y + 5 = -2 + 5 = 3<br />
\end{aligned}

    \begin{aligned}<br />
y + 3 &= 0 \\<br />
y &= -3 \\<br />
x &= y + 5 = -3 + 5 = 2<br />
\end{aligned}

    3. x=3, y=-2; x=2, y=-3

    01
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