Solve 0.1=3y(0.9/1.1-x/sqrt{10^7})-1

$$0.1=3y( \frac{ 0.9 }{ 1.1 } - \frac{ x }{ \sqrt{ { 10 }^{ 7 } } } )-1$$

Solve for x

$$x=\frac{100\sqrt{10}\left(270y-121\right)}{33y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Expand \frac{0.9}{1.1} by multiplying both numerator and the denominator by 10.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{\sqrt{10^{7}}}\right)-1$$

Calculate 10 to the power of 7 and get 10000000.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{\sqrt{10000000}}\right)-1$$

Factor 10000000=1000^{2}\times 10. Rewrite the square root of the product \sqrt{1000^{2}\times 10} as the product of square roots \sqrt{1000^{2}}\sqrt{10}. Take the square root of 1000^{2}.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{1000\sqrt{10}}\right)-1$$

Rationalize the denominator of \frac{x}{1000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{1000\left(\sqrt{10}\right)^{2}}\right)-1$$

The square of \sqrt{10} is 10.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{1000\times 10}\right)-1$$

Multiply 1000 and 10 to get 10000.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{10000}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11 and 10000 is 110000. Multiply \frac{9}{11} times \frac{10000}{10000}. Multiply \frac{x\sqrt{10}}{10000} times \frac{11}{11}.

$$0.1=3y\left(\frac{9\times 10000}{110000}-\frac{11x\sqrt{10}}{110000}\right)-1$$

Since \frac{9\times 10000}{110000} and \frac{11x\sqrt{10}}{110000} have the same denominator, subtract them by subtracting their numerators.

$$0.1=3y\times \frac{9\times 10000-11x\sqrt{10}}{110000}-1$$

Do the multiplications in 9\times 10000-11x\sqrt{10}.

$$0.1=3y\times \frac{90000-11x\sqrt{10}}{110000}-1$$

Express 3\times \frac{90000-11x\sqrt{10}}{110000} as a single fraction.

$$0.1=\frac{3\left(90000-11x\sqrt{10}\right)}{110000}y-1$$

Use the distributive property to multiply 3 by 90000-11x\sqrt{10}.

$$0.1=\frac{270000-33\sqrt{10}x}{110000}y-1$$

Express \frac{270000-33\sqrt{10}x}{110000}y as a single fraction.

$$0.1=\frac{\left(270000-33\sqrt{10}x\right)y}{110000}-1$$

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

$$\frac{\left(270000-33\sqrt{10}x\right)y}{110000}-1=0.1$$

Use the distributive property to multiply 270000-33\sqrt{10}x by y.

$$\frac{270000y-33\sqrt{10}xy}{110000}-1=0.1$$

Add 1 to both sides.

$$\frac{270000y-33\sqrt{10}xy}{110000}=0.1+1$$

Add 0.1 and 1 to get 1.1.

$$\frac{270000y-33\sqrt{10}xy}{110000}=1.1$$

Multiply both sides by 110000.

$$270000y-33\sqrt{10}xy=1.1\times 110000$$

Multiply 1.1 and 110000 to get 121000.

$$270000y-33\sqrt{10}xy=121000$$

Subtract 270000y from both sides.

$$-33\sqrt{10}xy=121000-270000y$$

The equation is in standard form.

$$\left(-33\sqrt{10}y\right)x=121000-270000y$$

Divide both sides by -33\sqrt{10}y.

$$\frac{\left(-33\sqrt{10}y\right)x}{-33\sqrt{10}y}=\frac{121000-270000y}{-33\sqrt{10}y}$$

Dividing by -33\sqrt{10}y undoes the multiplication by -33\sqrt{10}y.

$$x=\frac{121000-270000y}{-33\sqrt{10}y}$$

Divide 121000-270000y by -33\sqrt{10}y.

$$x=-\frac{100\sqrt{10}\left(121-270y\right)}{33y}$$

Solve for y

$$y=\frac{121000}{3\left(-11\sqrt{10}x+90000\right)}$$

$$x\neq \frac{9000\sqrt{10}}{11}$$

Steps for Solving Linear Equation

Expand \frac{0.9}{1.1} by multiplying both numerator and the denominator by 10.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{\sqrt{10^{7}}}\right)-1$$

Calculate 10 to the power of 7 and get 10000000.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{\sqrt{10000000}}\right)-1$$

Factor 10000000=1000^{2}\times 10. Rewrite the square root of the product \sqrt{1000^{2}\times 10} as the product of square roots \sqrt{1000^{2}}\sqrt{10}. Take the square root of 1000^{2}.

$$0.1=3y\left(\frac{9}{11}-\frac{x}{1000\sqrt{10}}\right)-1$$

Rationalize the denominator of \frac{x}{1000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{1000\left(\sqrt{10}\right)^{2}}\right)-1$$

The square of \sqrt{10} is 10.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{1000\times 10}\right)-1$$

Multiply 1000 and 10 to get 10000.

$$0.1=3y\left(\frac{9}{11}-\frac{x\sqrt{10}}{10000}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11 and 10000 is 110000. Multiply \frac{9}{11} times \frac{10000}{10000}. Multiply \frac{x\sqrt{10}}{10000} times \frac{11}{11}.

$$0.1=3y\left(\frac{9\times 10000}{110000}-\frac{11x\sqrt{10}}{110000}\right)-1$$

Since \frac{9\times 10000}{110000} and \frac{11x\sqrt{10}}{110000} have the same denominator, subtract them by subtracting their numerators.

$$0.1=3y\times \frac{9\times 10000-11x\sqrt{10}}{110000}-1$$

Do the multiplications in 9\times 10000-11x\sqrt{10}.

$$0.1=3y\times \frac{90000-11\sqrt{10}x}{110000}-1$$

Express 3\times \frac{90000-11\sqrt{10}x}{110000} as a single fraction.

$$0.1=\frac{3\left(90000-11\sqrt{10}x\right)}{110000}y-1$$

Use the distributive property to multiply 3 by 90000-11\sqrt{10}x.

$$0.1=\frac{270000-33\sqrt{10}x}{110000}y-1$$

Express \frac{270000-33\sqrt{10}x}{110000}y as a single fraction.

$$0.1=\frac{\left(270000-33\sqrt{10}x\right)y}{110000}-1$$

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

$$\frac{\left(270000-33\sqrt{10}x\right)y}{110000}-1=0.1$$

Use the distributive property to multiply 270000-33\sqrt{10}x by y.

$$\frac{270000y-33\sqrt{10}xy}{110000}-1=0.1$$

Add 1 to both sides.

$$\frac{270000y-33\sqrt{10}xy}{110000}=0.1+1$$

Add 0.1 and 1 to get 1.1.

$$\frac{270000y-33\sqrt{10}xy}{110000}=1.1$$

Multiply both sides by 110000.

$$270000y-33\sqrt{10}xy=1.1\times 110000$$

Multiply 1.1 and 110000 to get 121000.

$$270000y-33\sqrt{10}xy=121000$$

Combine all terms containing y.

$$\left(270000-33\sqrt{10}x\right)y=121000$$

The equation is in standard form.

$$\left(-33\sqrt{10}x+270000\right)y=121000$$

Divide both sides by 270000-33\sqrt{10}x.

$$\frac{\left(-33\sqrt{10}x+270000\right)y}{-33\sqrt{10}x+270000}=\frac{121000}{-33\sqrt{10}x+270000}$$

Dividing by 270000-33\sqrt{10}x undoes the multiplication by 270000-33\sqrt{10}x.

$$y=\frac{121000}{-33\sqrt{10}x+270000}$$

Divide 121000 by 270000-33\sqrt{10}x.

$$y=\frac{121000}{3\left(-11\sqrt{10}x+90000\right)}$$