Solve {l}{2137x=y}{77/100y+2137=y}

$$\left. \begin{array} { l } { 2137 x = y } \\ { \frac { 77 } { 100 } y + 2137 = y } \end{array} \right.$$

Solve for x, y

$$x = \frac{100}{23} = 4\frac{8}{23} \approx 4.347826087$$

$$y = \frac{213700}{23} = 9291\frac{7}{23} \approx 9291.304347826$$

Solution Steps

Consider the second equation. Subtract y from both sides.

$$\frac{77}{100}y+2137-y=0$$

Combine \frac{77}{100}y and -y to get -\frac{23}{100}y.

$$-\frac{23}{100}y+2137=0$$

Subtract 2137 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{23}{100}y=-2137$$

Multiply both sides by -\frac{100}{23}, the reciprocal of -\frac{23}{100}.

$$y=-2137\left(-\frac{100}{23}\right)$$

Multiply -2137 and -\frac{100}{23} to get \frac{213700}{23}.

$$y=\frac{213700}{23}$$

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

$$2137x=\frac{213700}{23}$$

Divide both sides by 2137.

$$x=\frac{\frac{213700}{23}}{2137}$$

Express \frac{\frac{213700}{23}}{2137} as a single fraction.

$$x=\frac{213700}{23\times 2137}$$

Multiply 23 and 2137 to get 49151.

$$x=\frac{213700}{49151}$$

Reduce the fraction \frac{213700}{49151} to lowest terms by extracting and canceling out 2137.

$$x=\frac{100}{23}$$

The system is now solved.

$$x=\frac{100}{23} y=\frac{213700}{23}$$