1. ## 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. $x^3-y^3=35$
$x-y=5$

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

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

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

2. Is there a typo in #1?

Originally Posted by cloud5
3. $x^3-y^3=35$
$x-y=5$
Solve by substitution.
\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}

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

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

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

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