To eliminate the y terms for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation 4x - 3y = 34 second equation 3x + 2y = 17 The first equation should be multiplied by 2 and the second equation by 3. The first equation should be multiplied by w and the second equation by -3 This first equation should be multiplied by 3 and the second equation by 4 The first equation should be multiplied by 3 and second equation by 4

people went from manufacturing one object at a time by hand to manufacturing many objects in factories

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)