Solve the system: y = 3x + 5 and x = -2y - 4 Answer in this format: (x, y) NO spaces in your answer Enter Answer were BUITIONSWER

-2,-1

Step-by-step explanation:

Solve the following system:

{y = 3 x + 5 | (equation 1)

x = -2 y - 4 | (equation 2)

Express the system in standard form:

{-(3 x) + y = 5 | (equation 1)

x + 2 y = -4 | (equation 2)

Add 1/3 × (equation 1) to equation 2:

{-(3 x) + y = 5 | (equation 1)

0 x+(7 y)/3 = -7/3 | (equation 2)

Multiply equation 2 by 3/7:

{-(3 x) + y = 5 | (equation 1)

0 x+y = -1 | (equation 2)

Subtract equation 2 from equation 1:

{-(3 x)+0 y = 6 | (equation 1)

0 x+y = -1 | (equation 2)

Divide equation 1 by -3:

{x+0 y = -2 | (equation 1)

0 x+y = -1 | (equation 2)

Collect results:

{x = -2 , y = -1

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8

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