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

Feb 21, 2018

$A = 3 x - 5 \text{ and } B = 3 - x$

#### Explanation:

$A + B = 2 x - 2 \to \left(1\right)$

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

$\left(1\right) + \left(2\right) \text{ term by term to eliminate B}$

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

$\Rightarrow 2 A = 6 x - 10$

$\text{divide both sides by 2}$

$\Rightarrow A = \frac{1}{2} \left(6 x - 10\right) = 3 x - 5$

$\text{substitute "A=3x-5" in equation } \left(1\right)$

$3 x - 5 + B = 2 x - 2$

$\text{subtract " (3x-5)" from both sides}$

$\Rightarrow B = 2 x - 2 - 3 x + 5 = 3 - x$

$\textcolor{b l u e}{\text{As a check}}$

$A - B = 3 x - 5 - 3 + x = 4 x - 8 \text{ correct}$