Solve {l}{6=a+11b}{2=77a+903}

$$\left. \begin{array} { l } { 6 = a + 11 b } \\ { 2 = 77 a + 903 } \end{array} \right.$$

Solve for a, b

$$a = -\frac{901}{77} = -11\frac{54}{77} \approx -11.701298701$$

$$b = \frac{1363}{847} = 1\frac{516}{847} \approx 1.609208973$$

Solution Steps

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$77a+903=2$$

Subtract 903 from both sides.

$$77a=2-903$$

Subtract 903 from 2 to get -901.

$$77a=-901$$

Divide both sides by 77.

$$a=-\frac{901}{77}$$

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

$$6=-\frac{901}{77}+11b$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{901}{77}+11b=6$$

Add \frac{901}{77} to both sides.

$$11b=6+\frac{901}{77}$$

Add 6 and \frac{901}{77} to get \frac{1363}{77}.

$$11b=\frac{1363}{77}$$

Divide both sides by 11.

$$b=\frac{\frac{1363}{77}}{11}$$

Express \frac{\frac{1363}{77}}{11} as a single fraction.

$$b=\frac{1363}{77\times 11}$$

Multiply 77 and 11 to get 847.

$$b=\frac{1363}{847}$$

The system is now solved.

$$a=-\frac{901}{77} b=\frac{1363}{847}$$