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

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

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

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

2. Is there a typo in #1?

Originally Posted by cloud5
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. $\displaystyle x=3, y=-2; x=2, y=-3$

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