Let's look at the second equation and try multiplying it by 4:
4 * (3x + ky) = 4 * 27
Which gives us:
12x + 4ky = 108
This looks almost exactly like the first equation except that instead of -20y, there is 4ky. We could try making them equal to each other and solving for k:
-20y = 4ky
-20 = 4k
k = -5
Then, the answer is k = -5.
Answer:

Step-by-step explanation:
f(x) + n - translation n units up
f(x) - n - translation n units down
f(x + n) - translation n units to the left
f(x - n) - translation n units to the right
We have

translation 1 unit up (f(x) + 1)

Let the price of the 3rd card be c. Now we can write the equation:
c + (c + 20) + (c + c + 20) = 160 .........(1)
Simplifying the left hand side of equation (1), we get:
4c + 40 = 160 .........(2)
Subtracting 40 from both sides of equation (2) gives:
4c = 120
from which c = $30.
Therefore the price of the second card = 30 + 20 = $50
and the price of the first card = 30 + 50 = $80.
J(x) is equivalent to Y. For example if you were to have a equation in slope intercept form it would be y=mx+b which can be written in the same way as your problem j(x)=mx+b. To sum it up j(x) is just another way to say y=