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

##### 1 Answer

Feb 21, 2018

#### Answer:

#### Explanation:

#A+B=2x-2to(1)#

#A-B=4x-8to(2)#

#(1)+(2)" term by term to eliminate B"#

#(A+A)+(B-B)=(2x+4x-2-8)#

#rArr2A=6x-10#

#"divide both sides by 2"#

#rArrA=1/2(6x-10)=3x-5#

#"substitute "A=3x-5" in equation "(1)#

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

#"subtract " (3x-5)" from both sides"#

#rArrB=2x-2-3x+5=3-x#

#color(blue)"As a check"#

#A-B=3x-5-3+x=4x-8" correct"#