SAT math question algebra, x y and C

Question

Given the system of equations: $\begin{cases} 5x+3y=3c\\ 2y = c-4x\end{cases}$

if $x+y=6$, then what is the value of $c$ which makes the system consistent?

Problem source: sat exam ivy global book

I began solving it as:

$9x+5y=4c$

$5x+5y=\dots$ (editor's note: illegible from here out)

link to original photo: https://i.stack.imgur.com/lNm3w.jpg

Answer 1

$$5x + 3y = 3c\tag{1}$$ $$2y = c - 4x\tag{2}$$

The second equation can be written $$4x + 2y = c\tag{2}$$

(Then I think you tried adding the equations.)

Try subtracting the second equation from the first equation, instead, to get $$x+y = 2c$$

Now, you're given that $x+y = 6$.

I think you can take it from here.

Answer 2

Equivalently: from 2y= c- 4x, y= (c/2)- 2x so that 5x+ 3y= 5x+ 3((c/2)- 2x)= 5x- -6x+ (3/2)c= -x+ (3/2)c= 3c so x= (3/2)c- 3x= -(3/2)c.