Solve {l}{12-9b+15-5b=14-8b+6}{4f+49-13f-78+23f=0}{13*(s-5)-4*(s-1)+s=5}

$$\left. \begin{array} { l } { 12 - 9 b + 15 - 5 b = 14 - 8 b + 6 } \\ { 4 f + 49 - 13 f - 78 + 23 f = 0 } \\ { 13 \cdot ( s - 5 ) - 4 \cdot ( s - 1 ) + s = 5 } \end{array} \right.$$

Solve for b, f, s

$$s = \frac{33}{5} = 6\frac{3}{5} = 6.6$$

$$b = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$f = \frac{29}{14} = 2\frac{1}{14} \approx 2.071428571$$

Solution Steps

Consider the first equation. Add 12 and 15 to get 27.

$$27-9b-5b=14-8b+6$$

Combine -9b and -5b to get -14b.

$$27-14b=14-8b+6$$

Add 14 and 6 to get 20.

$$27-14b=20-8b$$

Add 8b to both sides.

$$27-14b+8b=20$$

Combine -14b and 8b to get -6b.

$$27-6b=20$$

Subtract 27 from both sides.

$$-6b=20-27$$

Subtract 27 from 20 to get -7.

$$-6b=-7$$

Divide both sides by -6.

$$b=\frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$b=\frac{7}{6}$$

Consider the second equation. Combine 4f and -13f to get -9f.

$$-9f+49-78+23f=0$$

Subtract 78 from 49 to get -29.

$$-9f-29+23f=0$$

Combine -9f and 23f to get 14f.

$$14f-29=0$$

Add 29 to both sides. Anything plus zero gives itself.

$$14f=29$$

Divide both sides by 14.

$$f=\frac{29}{14}$$

Consider the third equation. Use the distributive property to multiply 13 by s-5.

$$13s-65-4\left(s-1\right)+s=5$$

Use the distributive property to multiply -4 by s-1.

$$13s-65-4s+4+s=5$$

Combine 13s and -4s to get 9s.

$$9s-65+4+s=5$$

Add -65 and 4 to get -61.

$$9s-61+s=5$$

Combine 9s and s to get 10s.

$$10s-61=5$$

Add 61 to both sides.

$$10s=5+61$$

Add 5 and 61 to get 66.

$$10s=66$$

Divide both sides by 10.

$$s=\frac{66}{10}$$

Reduce the fraction \frac{66}{10} to lowest terms by extracting and canceling out 2.

$$s=\frac{33}{5}$$

The system is now solved.

$$b=\frac{7}{6} f=\frac{29}{14} s=\frac{33}{5}$$