Solve {l}{x-2a=1}{x-3b=2}{x-4c=3}{x-5d=4}{x-6=5}{x-7f=0}

$$\left. \begin{array} { l } { x - 2 a = 1 } \\ { x - 3 b = 2 } \\ { x - 4 c = 3 } \\ { x - 5 d = 4 } \\ { x - 6 = 5 } \\ { x - 7 f = 0 } \end{array} \right.$$

Solve for x, a, b, c, d, f

$$x=11$$

$$a=5$$

$$b=3$$

$$c=2$$

$$d = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

$$f = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571$$

Solution Steps

Consider the fifth equation. Add 6 to both sides.

$$x=5+6$$

Add 5 and 6 to get 11.

$$x=11$$

Consider the equation (6). Insert the known values of variables into the equation.

$$11-7f=0$$

Subtract 11 from both sides. Anything subtracted from zero gives its negation.

$$-7f=-11$$

Divide both sides by -7.

$$f=\frac{-11}{-7}$$

Fraction \frac{-11}{-7} can be simplified to \frac{11}{7} by removing the negative sign from both the numerator and the denominator.

$$f=\frac{11}{7}$$

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

$$11-2a=1$$

Subtract 11 from both sides.

$$-2a=1-11$$

Subtract 11 from 1 to get -10.

$$-2a=-10$$

Divide both sides by -2.

$$a=\frac{-10}{-2}$$

Divide -10 by -2 to get 5.

$$a=5$$

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

$$11-3b=2$$

Subtract 11 from both sides.

$$-3b=2-11$$

Subtract 11 from 2 to get -9.

$$-3b=-9$$

Divide both sides by -3.

$$b=\frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$b=3$$

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

$$11-4c=3$$

Subtract 11 from both sides.

$$-4c=3-11$$

Subtract 11 from 3 to get -8.

$$-4c=-8$$

Divide both sides by -4.

$$c=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$c=2$$

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

$$11-5d=4$$

Subtract 11 from both sides.

$$-5d=4-11$$

Subtract 11 from 4 to get -7.

$$-5d=-7$$

Divide both sides by -5.

$$d=\frac{-7}{-5}$$

Fraction \frac{-7}{-5} can be simplified to \frac{7}{5} by removing the negative sign from both the numerator and the denominator.

$$d=\frac{7}{5}$$

The system is now solved.

$$x=11 a=5 b=3 c=2 d=\frac{7}{5} f=\frac{11}{7}$$