Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?

The cost of natural gas is $0.17 per unit.
The cost of natural gas is $0.20 per unit.
The cost of natural gas is $0.72 per unit.
The cost of natural gas is $0.83 per unit.

step-by-step explanation:

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)

4932,9180,7625 are divisible by 9

answer is 1

step-by-step explanation: