Solve {l}{79=0.22*x_{B}*0.87}{x_{A}+x_{B}=20}{a=x_{A}*0}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { 79 = 0.22 \cdot x_{B} \cdot 0.87 }\\ { x_{A} + x_{B} = 20 }\\ { a = x_{A} \cdot 0 }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x_B, x_A, a, b

$$b=0$$

Solution Steps

Consider the first equation. Multiply 0.22 and 0.87 to get 0.1914.

$$79=0.1914x_{B}$$

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

$$0.1914x_{B}=79$$

Divide both sides by 0.1914.

$$x_{B}=\frac{79}{0.1914}$$

Expand \frac{79}{0.1914} by multiplying both numerator and the denominator by 10000.

$$x_{B}=\frac{790000}{1914}$$

Reduce the fraction \frac{790000}{1914} to lowest terms by extracting and canceling out 2.

$$x_{B}=\frac{395000}{957}$$

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

$$x_{A}+\frac{395000}{957}=20$$

Subtract \frac{395000}{957} from both sides.

$$x_{A}=20-\frac{395000}{957}$$

Subtract \frac{395000}{957} from 20 to get -\frac{375860}{957}.

$$x_{A}=-\frac{375860}{957}$$

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

$$a=-\frac{375860}{957}\times 0$$

Multiply -\frac{375860}{957} and 0 to get 0.

$$a=0$$

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

$$b=0$$

The system is now solved.

$$x_{B}=\frac{395000}{957} x_{A}=-\frac{375860}{957} a=0 b=0$$