Solve {l}{a-9/3-a=-3/2}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { \frac{a - 9}{3 - a} = \frac{-3}{2} }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c=-9$$

Solution Steps

Consider the first equation. Variable a cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 2\left(a-3\right), the least common multiple of 3-a,2.

$$-2\left(a-9\right)=\left(a-3\right)\left(-3\right)$$

Use the distributive property to multiply -2 by a-9.

$$-2a+18=\left(a-3\right)\left(-3\right)$$

Use the distributive property to multiply a-3 by -3.

$$-2a+18=-3a+9$$

Add 3a to both sides.

$$-2a+18+3a=9$$

Combine -2a and 3a to get a.

$$a+18=9$$

Subtract 18 from both sides.

$$a=9-18$$

Subtract 18 from 9 to get -9.

$$a=-9$$

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

$$b=-9$$

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

$$c=-9$$

The system is now solved.

$$a=-9 b=-9 c=-9$$