Solve {l}{b+(b+5)-2(b-5)=18+b}{0.1(a-0.2)=1.2+2.4a}

$$\left. \begin{array} { l } { b + ( b + 5 ) - 2 ( b - 5 ) = 18 + b } \\ { 0.1 ( a - 0.2 ) = 1.2 + 2.4 a } \end{array} \right.$$

Solve for b, a

$$b=-3$$

$$a=-\frac{61}{115}\approx -0.530434783$$

Solution Steps

Consider the first equation. Combine b and b to get 2b.

$$2b+5-2\left(b-5\right)=18+b$$

Use the distributive property to multiply -2 by b-5.

$$2b+5-2b+10=18+b$$

Combine 2b and -2b to get 0.

$$5+10=18+b$$

Add 5 and 10 to get 15.

$$15=18+b$$

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

$$18+b=15$$

Subtract 18 from both sides.

$$b=15-18$$

Subtract 18 from 15 to get -3.

$$b=-3$$

Consider the second equation. Use the distributive property to multiply 0.1 by a-0.2.

$$0.1a-0.02=1.2+2.4a$$

Subtract 2.4a from both sides.

$$0.1a-0.02-2.4a=1.2$$

Combine 0.1a and -2.4a to get -2.3a.

$$-2.3a-0.02=1.2$$

Add 0.02 to both sides.

$$-2.3a=1.2+0.02$$

Add 1.2 and 0.02 to get 1.22.

$$-2.3a=1.22$$

Divide both sides by -2.3.

$$a=\frac{1.22}{-2.3}$$

Expand \frac{1.22}{-2.3} by multiplying both numerator and the denominator by 100.

$$a=\frac{122}{-230}$$

Reduce the fraction \frac{122}{-230} to lowest terms by extracting and canceling out 2.

$$a=-\frac{61}{115}$$

The system is now solved.

$$b=-3 a=-\frac{61}{115}$$