How can I solve this in substitution, can I have a step by step. (x, y)
y=2x+1
2x-y=3

First, you have to see if there is y= or x = to substitute for the equation to find the solution.

y = 2x + 1

Rewrite the equation in slope-intercept form.

2x - y = 3 ->  y = 2x + 3

Add both equations together.                            Substitute.

    2x+1                                                               2(1)+1 = y

+   2x+3                                                                 2 + 1 = y

                                                                                  y = 3

   y=  4x + 4

     4x =4

      x  = 1

Your answer should be (1,3).

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt