Which of these is a concept the romantics valued?
a. science
b. industrialism
c. idealism
d. immobility

I think the answer is C. Idealism. Idealism is a philosophy which centers on the man's idea and belief on the material things. Idealism helps men understand on how things came to be in the world. For many romantics, the idea of idealism helps them mold the rationality of man. It centers on how man can provide for himself as well as solve earthly problems

substitute y = 2x - 4 to x + 2y = 12:

x + 2(2x - 4) = 12     use distributive property

x + (2)(2x) + () = 12

x + 4x - 8 = 12     add 8 to both sides

5x = 20     divide both sides by 5

x = 4

put the value of x to the first equation:

y = 2(4) - 4

y = 8 - 4

y = 4

answer: x = 4 and y = 4