Solve y=frac{6+sqrt{21}}{6}x+1

$$y= \frac{ 6+ \sqrt{ 21 } }{ 6 } x+1$$

Solve for x

$$x=\frac{2\left(\sqrt{21}-6\right)\left(1-y\right)}{5}$$

Steps for Solving Linear Equation

Express \frac{6+\sqrt{21}}{6}x as a single fraction.

$$y=\frac{\left(6+\sqrt{21}\right)x}{6}+1$$

Use the distributive property to multiply 6+\sqrt{21} by x.

$$y=\frac{6x+\sqrt{21}x}{6}+1$$

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

$$\frac{6x+\sqrt{21}x}{6}+1=y$$

Subtract 1 from both sides.

$$\frac{6x+\sqrt{21}x}{6}=y-1$$

Multiply both sides of the equation by 6.

$$6x+\sqrt{21}x=6y-6$$

Combine all terms containing x.

$$\left(6+\sqrt{21}\right)x=6y-6$$

The equation is in standard form.

$$\left(\sqrt{21}+6\right)x=6y-6$$

Divide both sides by 6+\sqrt{21}.

$$\frac{\left(\sqrt{21}+6\right)x}{\sqrt{21}+6}=\frac{6y-6}{\sqrt{21}+6}$$

Dividing by 6+\sqrt{21} undoes the multiplication by 6+\sqrt{21}.

$$x=\frac{6y-6}{\sqrt{21}+6}$$

Divide -6+6y by 6+\sqrt{21}.

$$x=-\frac{2\left(\sqrt{21}-6\right)\left(y-1\right)}{5}$$

Solve for y

$$y=\frac{\sqrt{21}x}{6}+x+1$$