Solve {l}{x/990=8.89}{x/990-y=9.9}

$$\left. \begin{array} { l } { \frac { x } { 990 } = 8.89 } \\ { \frac { x } { 990 - y } = 9.9 } \end{array} \right.$$

Solve for x, y

$$x=8801.1$$

$$y=101$$

Solution Steps

Consider the first equation. Multiply both sides by 990.

$$x=8.89\times 990$$

Multiply 8.89 and 990 to get 8801.1.

$$x=8801.1$$

Consider the second equation. Insert the known values of variables into the equation.

$$\frac{8801.1}{990-y}=9.9$$

Variable y cannot be equal to 990 since division by zero is not defined. Multiply both sides of the equation by -y+990.

$$8801.1=9.9\left(-y+990\right)$$

Use the distributive property to multiply 9.9 by -y+990.

$$8801.1=-9.9y+9801$$

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

$$-9.9y+9801=8801.1$$

Subtract 9801 from both sides.

$$-9.9y=8801.1-9801$$

Subtract 9801 from 8801.1 to get -999.9.

$$-9.9y=-999.9$$

Divide both sides by -9.9.

$$y=\frac{-999.9}{-9.9}$$

Expand \frac{-999.9}{-9.9} by multiplying both numerator and the denominator by 10.

$$y=\frac{-9999}{-99}$$

Divide -9999 by -99 to get 101.

$$y=101$$

The system is now solved.

$$x=8801.1 y=101$$