Solve {l}{2006x+2001y=2005}{2016-2007y=6039}

$$\left\{ \begin{array} { l } { 2006 x + 2001 y = 2005 } \\ { 2016 - 2007 y = 6039 } \end{array} \right.$$

Solve for x, y

$$x = \frac{670781}{223669} = 2\frac{223443}{223669} \approx 2.998989578$$

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

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.

$$2006x+2001\left(-\frac{447}{223}\right)=2005$$

Multiply 2001 and -\frac{447}{223} to get -\frac{894447}{223}.

$$2006x-\frac{894447}{223}=2005$$

Add \frac{894447}{223} to both sides.

$$2006x=2005+\frac{894447}{223}$$

Add 2005 and \frac{894447}{223} to get \frac{1341562}{223}.

$$2006x=\frac{1341562}{223}$$

Divide both sides by 2006.

$$x=\frac{\frac{1341562}{223}}{2006}$$

Express \frac{\frac{1341562}{223}}{2006} as a single fraction.

$$x=\frac{1341562}{223\times 2006}$$

Multiply 223 and 2006 to get 447338.

$$x=\frac{1341562}{447338}$$

Reduce the fraction \frac{1341562}{447338} to lowest terms by extracting and canceling out 2.

$$x=\frac{670781}{223669}$$

The system is now solved.

$$x=\frac{670781}{223669} y=-\frac{447}{223}$$