Answer to Question #187597 in Algebra for Amesha

Question

given 4b-a=4 and ab=8 when the equations are solved for a and b simultaneously, one of the values of a is

Answer 1

We are gven the two equations as follows

4b-a=4 ......................(i)

ab=8 ..........................(ii)

from equation (ii), make a the subject of the formula as follows

ab=8

ab/b=8/b

a=8/b ........................(iii)

substitute the value of a in equation (i) as follows

4b-a=4

4b-8/b=4

multiply through by b

4b²-8=4b ...........(iv)

4b²-4b-8=0

divide through by 4

b²-b-2=0

(b-2)(b+1)=0

therefore b=2 or b=-1

find the roots of a using equation (iii) as follows

a=8/b

when b=2, then a=8/2 = 4

when b=-1, then a=8/-1=-8