Solve for x
x=-7\sqrt{5}y+16y+14-7\sqrt{5}
Solve for y
y=\frac{7\sqrt{5}x+16x+14\sqrt{5}+21}{11}
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\sqrt{5}x+2x+\left(3-2\sqrt{5}\right)y+7=0
Use the distributive property to multiply \sqrt{5}+2 by x.
\sqrt{5}x+2x+3y-2\sqrt{5}y+7=0
Use the distributive property to multiply 3-2\sqrt{5} by y.
\sqrt{5}x+2x-2\sqrt{5}y+7=-3y
Subtract 3y from both sides. Anything subtracted from zero gives its negation.
\sqrt{5}x+2x+7=-3y+2\sqrt{5}y
Add 2\sqrt{5}y to both sides.
\sqrt{5}x+2x=-3y+2\sqrt{5}y-7
Subtract 7 from both sides.
\left(\sqrt{5}+2\right)x=-3y+2\sqrt{5}y-7
Combine all terms containing x.
\left(\sqrt{5}+2\right)x=2\sqrt{5}y-3y-7
The equation is in standard form.
\frac{\left(\sqrt{5}+2\right)x}{\sqrt{5}+2}=\frac{2\sqrt{5}y-3y-7}{\sqrt{5}+2}
Divide both sides by \sqrt{5}+2.
x=\frac{2\sqrt{5}y-3y-7}{\sqrt{5}+2}
Dividing by \sqrt{5}+2 undoes the multiplication by \sqrt{5}+2.
x=\left(\sqrt{5}-2\right)\left(2\sqrt{5}y-3y-7\right)
Divide -3y+2\sqrt{5}y-7 by \sqrt{5}+2.
\sqrt{5}x+2x+\left(3-2\sqrt{5}\right)y+7=0
Use the distributive property to multiply \sqrt{5}+2 by x.
\sqrt{5}x+2x+3y-2\sqrt{5}y+7=0
Use the distributive property to multiply 3-2\sqrt{5} by y.
2x+3y-2\sqrt{5}y+7=-\sqrt{5}x
Subtract \sqrt{5}x from both sides. Anything subtracted from zero gives its negation.
3y-2\sqrt{5}y+7=-\sqrt{5}x-2x
Subtract 2x from both sides.
3y-2\sqrt{5}y=-\sqrt{5}x-2x-7
Subtract 7 from both sides.
-2\sqrt{5}y+3y=-\sqrt{5}x-2x-7
Reorder the terms.
\left(-2\sqrt{5}+3\right)y=-\sqrt{5}x-2x-7
Combine all terms containing y.
\left(3-2\sqrt{5}\right)y=-\sqrt{5}x-2x-7
The equation is in standard form.
\frac{\left(3-2\sqrt{5}\right)y}{3-2\sqrt{5}}=\frac{-\sqrt{5}x-2x-7}{3-2\sqrt{5}}
Divide both sides by 3-2\sqrt{5}.
y=\frac{-\sqrt{5}x-2x-7}{3-2\sqrt{5}}
Dividing by 3-2\sqrt{5} undoes the multiplication by 3-2\sqrt{5}.
y=\frac{7\sqrt{5}x+16x+14\sqrt{5}+21}{11}
Divide -\sqrt{5}x-2x-7 by 3-2\sqrt{5}.
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