Solve (8x+3y+57)/sqrt{8^2+3^2}=1

$$\frac { ( 8 x + 3 y + 57 ) } { \sqrt { 8 ^ { 2 } + 3 ^ { 2 } } } = 1$$

Solve for x

$$x=\frac{-3y+\sqrt{73}-57}{8}$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$\frac{8x+3y+57}{\sqrt{64+3^{2}}}=1$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x+3y+57}{\sqrt{64+9}}=1$$

Add 64 and 9 to get 73.

$$\frac{8x+3y+57}{\sqrt{73}}=1$$

Rationalize the denominator of \frac{8x+3y+57}{\sqrt{73}} by multiplying numerator and denominator by \sqrt{73}.

$$\frac{\left(8x+3y+57\right)\sqrt{73}}{\left(\sqrt{73}\right)^{2}}=1$$

The square of \sqrt{73} is 73.

$$\frac{\left(8x+3y+57\right)\sqrt{73}}{73}=1$$

Use the distributive property to multiply 8x+3y+57 by \sqrt{73}.

$$\frac{8x\sqrt{73}+3y\sqrt{73}+57\sqrt{73}}{73}=1$$

Multiply both sides by 73.

$$8x\sqrt{73}+3y\sqrt{73}+57\sqrt{73}=73$$

Subtract 3y\sqrt{73} from both sides.

$$8x\sqrt{73}+57\sqrt{73}=73-3y\sqrt{73}$$

Subtract 57\sqrt{73} from both sides.

$$8x\sqrt{73}=73-3y\sqrt{73}-57\sqrt{73}$$

The equation is in standard form.

$$8\sqrt{73}x=-3\sqrt{73}y+73-57\sqrt{73}$$

Divide both sides by 8\sqrt{73}.

$$\frac{8\sqrt{73}x}{8\sqrt{73}}=\frac{\sqrt{73}\left(-3y+\sqrt{73}-57\right)}{8\sqrt{73}}$$

Dividing by 8\sqrt{73} undoes the multiplication by 8\sqrt{73}.

$$x=\frac{\sqrt{73}\left(-3y+\sqrt{73}-57\right)}{8\sqrt{73}}$$

Divide \left(\sqrt{73}-3y-57\right)\sqrt{73} by 8\sqrt{73}.

$$x=\frac{-3y+\sqrt{73}-57}{8}$$

Solve for y

$$y=\frac{-8x+\sqrt{73}-57}{3}$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$\frac{8x+3y+57}{\sqrt{64+3^{2}}}=1$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x+3y+57}{\sqrt{64+9}}=1$$

Add 64 and 9 to get 73.

$$\frac{8x+3y+57}{\sqrt{73}}=1$$

Rationalize the denominator of \frac{8x+3y+57}{\sqrt{73}} by multiplying numerator and denominator by \sqrt{73}.

$$\frac{\left(8x+3y+57\right)\sqrt{73}}{\left(\sqrt{73}\right)^{2}}=1$$

The square of \sqrt{73} is 73.

$$\frac{\left(8x+3y+57\right)\sqrt{73}}{73}=1$$

Use the distributive property to multiply 8x+3y+57 by \sqrt{73}.

$$\frac{8x\sqrt{73}+3y\sqrt{73}+57\sqrt{73}}{73}=1$$

Multiply both sides by 73.

$$8x\sqrt{73}+3y\sqrt{73}+57\sqrt{73}=73$$

Subtract 8x\sqrt{73} from both sides.

$$3y\sqrt{73}+57\sqrt{73}=73-8x\sqrt{73}$$

Subtract 57\sqrt{73} from both sides.

$$3y\sqrt{73}=73-8x\sqrt{73}-57\sqrt{73}$$

The equation is in standard form.

$$3\sqrt{73}y=-8\sqrt{73}x+73-57\sqrt{73}$$

Divide both sides by 3\sqrt{73}.

$$\frac{3\sqrt{73}y}{3\sqrt{73}}=\frac{\sqrt{73}\left(-8x+\sqrt{73}-57\right)}{3\sqrt{73}}$$

Dividing by 3\sqrt{73} undoes the multiplication by 3\sqrt{73}.

$$y=\frac{\sqrt{73}\left(-8x+\sqrt{73}-57\right)}{3\sqrt{73}}$$

Divide \left(\sqrt{73}-8x-57\right)\sqrt{73} by 3\sqrt{73}.

$$y=-\frac{8x}{3}+\frac{\sqrt{73}}{3}-19$$