Ŵhat is the answer to this? Or any help please :)
2x+3y=13
4x-y=-2

X = 0.5 and Y = 4.

                               Hope this helps you hun

x=1/2 and y=4

Step-by-step explanation:

There are two ways to go about this problem.

1. Substitution

2. Elimination

Substitution Method:

rearrange one of the equations so that it is in terms of a variable.  I will rearrange the bottom equation which is 4x-y=-2  which can also be written as y=4x+2

Now we will plug that value of "y" into the first equation and get 2x + 3 *(4x+2)=13

Now we will solve for x

2x +12x+6=13

14x=7

x=7/14 or 1/2

Plug x into the the equation and solve for y

2(1/2) + 3y=13

3y=12

y=4

Check your answer by plugging both in to the second equation

4(1/2)-4=-2?

2-4=-2

-2=-2

Elimination Method:

In order to eliminate a term you need to have an x or y term that is equal or opposite so we can subtract or add both equations together.  To do this we will multiple the top equation by a factor of 2 and end up with: 4x+6y=26

Now we are going to subtract the bottom equation from the top

4x+6y=26

-

4x-y=-2

7y=28

y=4

Plug in to get x

4x-4=-2

4x=2

x=2/4 or 1/2

Check!

2(1/2) + 3(4) = 13?

1+12=13

13=13

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

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