Solve {l}{2006x+2007y=20}{2016-2007y=6039}

$$\left\{ \begin{array} { l } { 2006 x + 2007 y = 20 } \\ { 2016 - 2007 y = 6039 } \end{array} \right.$$

Solve for x, y

$$x = \frac{4043}{2006} = 2\frac{31}{2006} \approx 2.015453639$$

$$y = -\frac{447}{223} = -2\frac{1}{223} \approx -2.004484305$$

Solution Steps

Consider the second equation. Subtract 2016 from both sides.

$$-2007y=6039-2016$$

Subtract 2016 from 6039 to get 4023.

$$-2007y=4023$$

Divide both sides by -2007.

$$y=\frac{4023}{-2007}$$

Reduce the fraction \frac{4023}{-2007} to lowest terms by extracting and canceling out 9.

$$y=-\frac{447}{223}$$

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

$$2006x+2007\left(-\frac{447}{223}\right)=20$$

Multiply 2007 and -\frac{447}{223} to get -4023.

$$2006x-4023=20$$

Add 4023 to both sides.

$$2006x=20+4023$$

Add 20 and 4023 to get 4043.

$$2006x=4043$$

Divide both sides by 2006.

$$x=\frac{4043}{2006}$$

The system is now solved.

$$x=\frac{4043}{2006} y=-\frac{447}{223}$$