Solve either equation for either variable. Since the second one has y on its own, the easiest choice is to solve that for y.
-5x + y = 13 ⇒ y = 5x + 13
Now substitute this into the other equation to eliminate y and rewrite it entirely in terms of x :
-3x + 3y = 3 ⇒ -3x + 3 (5x + 13) = 3
Simplify and solve for x :
-3x + 15x + 39 = 3
12x = -36
x = -3
Substitute this into either original equation to solve for y. Plugging x = -3 into the first equation would give
-3 (-3) + 3y = 3
9 + 3y = 3
3y = -6
y = -2
So the solution to the system of equations is (x, y) = (-3, -2).
PART A:
The generic equation of the line is:
y-yo = m (x-xo)
First we look for the slope of the line:
m = (y2-y1) / (x2-x1)
m = ((5000) - (6000)) / (4-3)
m = -1000
Then, we substitute any point in the generic equation:
(xo, yo) = (4, 5000)
Substituting:
y-5000 = (- 1000) (x-4)
Rewriting:
y = -1000x + 4000 + 5000
y = -1000x + 9000
The equation is:
y = -1000x + 9000
PART B:
For the price of 3.50 we have:
y = -1000 * (3.5) +9000
y = 5500