Solve 312x+sqrt{72}y=731

$$312x+ \sqrt{ 72 } y = 731$$

Solve for x

$$x=-\frac{\sqrt{2}y}{52}+\frac{731}{312}$$

Steps for Solving Linear Equation

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$312x+6\sqrt{2}y=731$$

Subtract 6\sqrt{2}y from both sides.

$$312x=731-6\sqrt{2}y$$

The equation is in standard form.

$$312x=-6\sqrt{2}y+731$$

Divide both sides by 312.

$$\frac{312x}{312}=\frac{-6\sqrt{2}y+731}{312}$$

Dividing by 312 undoes the multiplication by 312.

$$x=\frac{-6\sqrt{2}y+731}{312}$$

Divide 731-6\sqrt{2}y by 312.

$$x=-\frac{\sqrt{2}y}{52}+\frac{731}{312}$$

Solve for y

$$y=-\frac{\sqrt{2}\left(312x-731\right)}{12}$$

Steps for Solving Linear Equation

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$312x+6\sqrt{2}y=731$$

Subtract 312x from both sides.

$$6\sqrt{2}y=731-312x$$

Divide both sides by 6\sqrt{2}.

$$\frac{6\sqrt{2}y}{6\sqrt{2}}=\frac{731-312x}{6\sqrt{2}}$$

Dividing by 6\sqrt{2} undoes the multiplication by 6\sqrt{2}.

$$y=\frac{731-312x}{6\sqrt{2}}$$

Divide 731-312x by 6\sqrt{2}.

$$y=\frac{\sqrt{2}\left(731-312x\right)}{12}$$