Solve {l}{2x+1.6y=124}{2.6x+2.1=36}

$$\left\{ \begin{array} { l } { 2 x + 1.6 y = 124 } \\ { 2.6 x + 2.1 = 36 } \end{array} \right.$$

Solve for x, y

$$x = \frac{339}{26} = 13\frac{1}{26} \approx 13.038461538$$

$$y = \frac{6365}{104} = 61\frac{21}{104} \approx 61.201923077$$

Solution Steps

Consider the second equation. Subtract 2.1 from both sides.

$$2.6x=36-2.1$$

Subtract 2.1 from 36 to get 33.9.

$$2.6x=33.9$$

Divide both sides by 2.6.

$$x=\frac{33.9}{2.6}$$

Expand \frac{33.9}{2.6} by multiplying both numerator and the denominator by 10.

$$x=\frac{339}{26}$$

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

$$2\times \frac{339}{26}+1.6y=124$$

Multiply 2 and \frac{339}{26} to get \frac{339}{13}.

$$\frac{339}{13}+1.6y=124$$

Subtract \frac{339}{13} from both sides.

$$1.6y=124-\frac{339}{13}$$

Subtract \frac{339}{13} from 124 to get \frac{1273}{13}.

$$1.6y=\frac{1273}{13}$$

Divide both sides by 1.6.

$$y=\frac{\frac{1273}{13}}{1.6}$$

Express \frac{\frac{1273}{13}}{1.6} as a single fraction.

$$y=\frac{1273}{13\times 1.6}$$

Multiply 13 and 1.6 to get 20.8.

$$y=\frac{1273}{20.8}$$

Expand \frac{1273}{20.8} by multiplying both numerator and the denominator by 10.

$$y=\frac{12730}{208}$$

Reduce the fraction \frac{12730}{208} to lowest terms by extracting and canceling out 2.

$$y=\frac{6365}{104}$$

The system is now solved.

$$x=\frac{339}{26} y=\frac{6365}{104}$$