There's more ways than one to solve this, just as there's more ways than one to skin a cat.
Two paralle lines have the same slope, so the desired new line looks exactly like the given line 3x + 5y = 6, except that the constant, 6, is replaced by another value.
Write out 3x + 5y = c
Replace x with 0 and y with 3. Then 3(0) + 5(3) = c, and c = 15.
Thus, the equation of the new, parallel, line is 3x + 5y = 15.
Answer:
She will have paid $168 not including the original $75 and $243 with.
Answer:
(3,-1)
Step-by-step explanation:
So we have the system of equations:

As directed, add straight down. The y-variable will cancel:

Now, divide both sides by 5. The left cancels:

So x is 3.
Now, substitute 3 for x in either of the equations:

Substitute 3 for x:

Multiply:

Subtract 9 from both sides:

So, our answer is: x=3, y=-1 or (3,-1).
And we are done :)
This expression is already simplified.