Use the algebraic method of substitution to determine the point of intersection

Question

I thought I understood substitution to require two like terms in each equation, as in the following:

x+y=12

y=3x+4

How then does the following substitution work as taken from the answer section of my grade 10 math course when R and C are not present in both equations?

r=n

c=0.5n+450

let r =c (*this is what I don't understand - I was taught thus far that for r to equal c it would require that c were present in the first equation).

2n=0.5n+450...I understand the rest pretty much.

Thanks!

Answer 1

x+y = 12

y= 3x + 4

x+ 3x+4 = 12

4x = 8

x = 2

y =10

r=n

c=0.5n + 450

if r=c, then

n=0.5n +450

subtract 0.5n from both sides to get

0.5n =450

multiply both sides by 2

n = 900

r=900

c=900

r=c=n=900