Equations with literal coefficients

EQUATIONS WITH LITERAL COEFFICIENTS:

As stated earlier, the first letters of the alphabet usually represent known quantities (constants), and the last letters represent unknown quantities (variables). Thus, we usually solve for x, y , or 2.

An equation such as

ax - 8 = bx - 5

has letters as coefficients. Equations with literal coefficients are solved in the same way as equations with numerical coefficients, except that when an operation cannot actually be performed, it merely is indicated.

In solving for x in the equation

ax - 8 =bx-5

subtract bx from both members and add 8 to both members. The result is

ax - bx = 8 - 5

Since the subtraction on the left side cannot actually be performed, it is indicated. The quantity, a - b, is the coefficient of x when terms are collected. The equation takes the form

(a - b) x = 3

Now divide both sides of the equation by a-b. Again the result can be only indicated. The solution of the equation is

In solving for y in the equation

ay + b = 4

subtract b from both members as follows:

ay = 4 - b

Dividing both members by a, the solution is