Solve {l}{177x+86y=246}{123x+2014=354}

$$\left\{ \begin{array} { l } { 177 x + 86 y = 246 } \\ { 123 x + 2014 = 354 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{1660}{123} = -13\frac{61}{123} \approx -13.495934959$$

$$y = \frac{54013}{1763} = 30\frac{1123}{1763} \approx 30.636982416$$

Solution Steps

Consider the second equation. Subtract 2014 from both sides.

$$123x=354-2014$$

Subtract 2014 from 354 to get -1660.

$$123x=-1660$$

Divide both sides by 123.

$$x=-\frac{1660}{123}$$

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

$$177\left(-\frac{1660}{123}\right)+86y=246$$

Multiply 177 and -\frac{1660}{123} to get -\frac{97940}{41}.

$$-\frac{97940}{41}+86y=246$$

Add \frac{97940}{41} to both sides.

$$86y=246+\frac{97940}{41}$$

Add 246 and \frac{97940}{41} to get \frac{108026}{41}.

$$86y=\frac{108026}{41}$$

Divide both sides by 86.

$$y=\frac{\frac{108026}{41}}{86}$$

Express \frac{\frac{108026}{41}}{86} as a single fraction.

$$y=\frac{108026}{41\times 86}$$

Multiply 41 and 86 to get 3526.

$$y=\frac{108026}{3526}$$

Reduce the fraction \frac{108026}{3526} to lowest terms by extracting and canceling out 2.

$$y=\frac{54013}{1763}$$

The system is now solved.

$$x=-\frac{1660}{123} y=\frac{54013}{1763}$$