Solve {l}{b=-2a}{-22a+20=0}{c=10a-25}

$$\left\{ \begin{array} { l } { b = - 2 a } \\ { - 22 a + 20 = 0 } \\ { c = 10 a - 25 } \end{array} \right.$$

Solve for b, a, c

$$b = -\frac{20}{11} = -1\frac{9}{11} \approx -1.818181818$$

$$a=\frac{10}{11}\approx 0.909090909$$

$$c = -\frac{175}{11} = -15\frac{10}{11} \approx -15.909090909$$

Solution Steps

Consider the second equation. Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-22a=-20$$

Divide both sides by -22.

$$a=\frac{-20}{-22}$$

Reduce the fraction \frac{-20}{-22} to lowest terms by extracting and canceling out -2.

$$a=\frac{10}{11}$$

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

$$c=10\times \frac{10}{11}-25$$

Multiply 10 and \frac{10}{11} to get \frac{100}{11}.

$$c=\frac{100}{11}-25$$

Subtract 25 from \frac{100}{11} to get -\frac{175}{11}.

$$c=-\frac{175}{11}$$

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

$$b=-2\times \frac{10}{11}$$

Multiply -2 and \frac{10}{11} to get -\frac{20}{11}.

$$b=-\frac{20}{11}$$

The system is now solved.

$$b=-\frac{20}{11} a=\frac{10}{11} c=-\frac{175}{11}$$