Solve {l}{7f+(12+13f)-4*(6f-12)=2*(2f+3)+6*(3f+4)+6}{104b-(70-80b)+12*(5b+10)=78b-(2b-26)}

$$\left. \begin{array} { l } { 7 f + ( 12 + 13 f ) - 4 \cdot ( 6 f - 12 ) = 2 \cdot ( 2 f + 3 ) + 6 \cdot ( 3 f + 4 ) + 6 } \\ { 104 b - ( 70 - 80 b ) + 12 \cdot ( 5 b + 10 ) = 78 b - ( 2 b - 26 ) } \end{array} \right.$$

Solve for f, b

$$f=\frac{12}{13}\approx 0.923076923$$

$$b=-\frac{1}{7}\approx -0.142857143$$

Solution Steps

Consider the first equation. Combine 7f and 13f to get 20f.

$$20f+12-4\left(6f-12\right)=2\left(2f+3\right)+6\left(3f+4\right)+6$$

Use the distributive property to multiply -4 by 6f-12.

$$20f+12-24f+48=2\left(2f+3\right)+6\left(3f+4\right)+6$$

Combine 20f and -24f to get -4f.

$$-4f+12+48=2\left(2f+3\right)+6\left(3f+4\right)+6$$

Add 12 and 48 to get 60.

$$-4f+60=2\left(2f+3\right)+6\left(3f+4\right)+6$$

Use the distributive property to multiply 2 by 2f+3.

$$-4f+60=4f+6+6\left(3f+4\right)+6$$

Use the distributive property to multiply 6 by 3f+4.

$$-4f+60=4f+6+18f+24+6$$

Combine 4f and 18f to get 22f.

$$-4f+60=22f+6+24+6$$

Add 6 and 24 to get 30.

$$-4f+60=22f+30+6$$

Add 30 and 6 to get 36.

$$-4f+60=22f+36$$

Subtract 22f from both sides.

$$-4f+60-22f=36$$

Combine -4f and -22f to get -26f.

$$-26f+60=36$$

Subtract 60 from both sides.

$$-26f=36-60$$

Subtract 60 from 36 to get -24.

$$-26f=-24$$

Divide both sides by -26.

$$f=\frac{-24}{-26}$$

Reduce the fraction \frac{-24}{-26} to lowest terms by extracting and canceling out -2.

$$f=\frac{12}{13}$$

Consider the second equation. To find the opposite of 70-80b, find the opposite of each term.

$$104b-70+80b+12\left(5b+10\right)=78b-\left(2b-26\right)$$

Combine 104b and 80b to get 184b.

$$184b-70+12\left(5b+10\right)=78b-\left(2b-26\right)$$

Use the distributive property to multiply 12 by 5b+10.

$$184b-70+60b+120=78b-\left(2b-26\right)$$

Combine 184b and 60b to get 244b.

$$244b-70+120=78b-\left(2b-26\right)$$

Add -70 and 120 to get 50.

$$244b+50=78b-\left(2b-26\right)$$

To find the opposite of 2b-26, find the opposite of each term.

$$244b+50=78b-2b+26$$

Combine 78b and -2b to get 76b.

$$244b+50=76b+26$$

Subtract 76b from both sides.

$$244b+50-76b=26$$

Combine 244b and -76b to get 168b.

$$168b+50=26$$

Subtract 50 from both sides.

$$168b=26-50$$

Subtract 50 from 26 to get -24.

$$168b=-24$$

Divide both sides by 168.

$$b=\frac{-24}{168}$$

Reduce the fraction \frac{-24}{168} to lowest terms by extracting and canceling out 24.

$$b=-\frac{1}{7}$$

The system is now solved.

$$f=\frac{12}{13} b=-\frac{1}{7}$$