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Solve the simultaneous equations $x=2y$ and $x^2-5xy=-24$
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Solve the simultaneous equations $x=2y$ and $x^2&minus;5xy=&minus;24$

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Since $x=2y$ in the first equation, substitute for $x$ in the second equation

$(2y)^2-5(2y)y=-24$

removing brackets yields

$4y^2-10y^2=-24$

which simplifies to

$-6y^2=-24$

dividing both sides by $-6$ gives

$y^2=4$

square-root both sides

$\sqrt{y^2}=\pm \sqrt{4}$

therefore $y=2$ or $y=-2$

Remember that $x=2y$

so $x=4$ when $y=2$ and $x=-4$ when $y=-2$
by Diamond (61,678 points)

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