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Thread: Simultaneous Equation I

  1. #1
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    Simultaneous Equation I

    Help me to solve this please?

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

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

    3. $\displaystyle x^3-y^3=35$
    $\displaystyle x-y=5$

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

    2. $\displaystyle x=4, y=3, z=3$

    3. $\displaystyle x=3, y=-2; x=2, y=-3$
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  2. #2
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    Is there a typo in #1?

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

    $\displaystyle \begin{aligned}
    y + 2 &= 0 \\
    y &= -2 \\
    x &= y + 5 = -2 + 5 = 3
    \end{aligned}$

    $\displaystyle \begin{aligned}
    y + 3 &= 0 \\
    y &= -3 \\
    x &= y + 5 = -3 + 5 = 2
    \end{aligned}$

    3. $\displaystyle x=3, y=-2; x=2, y=-3$

    01
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