Solve y-1/sqrt{2}=-frac{sqrt{2}}{2}(x-pi/4)

$$y - \frac { 1 } { \sqrt { 2 } } = - \frac { \sqrt { 2 } } { 2 } ( x - \frac { \pi } { 4 } )$$

Solve for x

$$x=\frac{-4\sqrt{2}y+\pi +4}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$4y-2\times 2^{\frac{1}{2}}=4\left(-\frac{\sqrt{2}}{2}\right)\left(x-\frac{\pi }{4}\right)$$

Cancel out 2, the greatest common factor in 4 and 2.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}\left(x-\frac{\pi }{4}\right)$$

Use the distributive property to multiply -2\sqrt{2} by x-\frac{\pi }{4} and combine like terms.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x-2\sqrt{2}\left(-\frac{\pi }{4}\right)$$

Multiply -2 and -1 to get 2.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+2\sqrt{2}\times \frac{\pi }{4}$$

Express \sqrt{2}\times \frac{\pi }{4} as a single fraction.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+2\times \frac{\sqrt{2}\pi }{4}$$

Cancel out 4, the greatest common factor in 2 and 4.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+\frac{\sqrt{2}\pi }{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-2\sqrt{2}x+\frac{\sqrt{2}\pi }{2}=4y-2\times 2^{\frac{1}{2}}$$

Subtract \frac{\sqrt{2}\pi }{2} from both sides.

$$-2\sqrt{2}x=4y-2\times 2^{\frac{1}{2}}-\frac{\sqrt{2}\pi }{2}$$

Multiply both sides of the equation by 2.

$$-4\sqrt{2}x=8y-4\times 2^{\frac{1}{2}}-\sqrt{2}\pi$$

Reorder the terms.

$$-4\sqrt{2}x=8y-\pi \sqrt{2}-4\sqrt{2}$$

The equation is in standard form.

$$\left(-4\sqrt{2}\right)x=8y-\pi \sqrt{2}-4\sqrt{2}$$

Divide both sides by -4\sqrt{2}.

$$\frac{\left(-4\sqrt{2}\right)x}{-4\sqrt{2}}=\frac{8y-\pi \sqrt{2}-4\sqrt{2}}{-4\sqrt{2}}$$

Dividing by -4\sqrt{2} undoes the multiplication by -4\sqrt{2}.

$$x=\frac{8y-\pi \sqrt{2}-4\sqrt{2}}{-4\sqrt{2}}$$

Divide 8y-\pi \sqrt{2}-4\sqrt{2} by -4\sqrt{2}.

$$x=-\sqrt{2}y+\frac{\pi }{4}+1$$

Solve for y

$$y=-\frac{\sqrt{2}\left(4x-\pi -4\right)}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$4y-2\times 2^{\frac{1}{2}}=4\left(-\frac{\sqrt{2}}{2}\right)\left(x-\frac{\pi }{4}\right)$$

Cancel out 2, the greatest common factor in 4 and 2.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}\left(x-\frac{\pi }{4}\right)$$

Use the distributive property to multiply -2\sqrt{2} by x-\frac{\pi }{4} and combine like terms.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x-2\sqrt{2}\left(-\frac{\pi }{4}\right)$$

Multiply -2 and -1 to get 2.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+2\sqrt{2}\times \frac{\pi }{4}$$

Express \sqrt{2}\times \frac{\pi }{4} as a single fraction.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+2\times \frac{\sqrt{2}\pi }{4}$$

Cancel out 4, the greatest common factor in 2 and 4.

$$4y-2\times 2^{\frac{1}{2}}=-2\sqrt{2}x+\frac{\sqrt{2}\pi }{2}$$

Add 2\times 2^{\frac{1}{2}} to both sides.

$$4y=-2\sqrt{2}x+\frac{\sqrt{2}\pi }{2}+2\times 2^{\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$4y=-2\sqrt{2}x+\frac{\sqrt{2}\pi }{2}+2^{\frac{3}{2}}$$

Multiply both sides of the equation by 2.

$$8y=-4\sqrt{2}x+\sqrt{2}\pi +2\times 2^{\frac{3}{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and \frac{3}{2} to get \frac{5}{2}.

$$8y=-4\sqrt{2}x+\sqrt{2}\pi +2^{\frac{5}{2}}$$

The equation is in standard form.

$$8y=-4\sqrt{2}x+\pi \sqrt{2}+4\sqrt{2}$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{\sqrt{2}\left(4+\pi -4x\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{\sqrt{2}\left(4+\pi -4x\right)}{8}$$