# Suppose A and B represent linear expressions. If A+ B=2x -2 and A -B=4x-8, how do you find A and B?

Mar 14, 2018

$A = 3 x - 5 , B = 3 - x$

#### Explanation:

A+B=2x-2 ; (1) , A-B=4x-8 ; (2)

Adding equations (1) and (2) we get,

$A + \cancel{B} + A - \cancel{B} = 2 x - 2 + 4 x - 8$ or

$2 A = 6 x - 10 \therefore A = 3 x - 5$

Subtracting equation (2) from equation (1) we get,

$A + B - \left(A - B\right) = 2 x - 2 - \left(4 x - 8\right)$ or

$\cancel{A} + B - \cancel{A} + B = 2 x - 2 - 4 x + 8$ or

$2 B = - 2 x + 6 \therefore B = - x + 3$

Therefore, $A = 3 x - 5 , B = 3 - x$ [Ans]