3x + 7y=47
-4x + 7y=19

x = 4

y = 5

Step-by-step explanation:

For the longest time, struggled with systems of equations, but once I got them, they're all surprisingly easy- they're (usually) solved through the same methods, constantly.

The first thing to notice about your question is that there are 2 terms that are exactly the same, which is 7y. This means that you can use the "elimination" method to solve it, which is (in my opinion) the easiest one. What you do is subtract the 1st equation by the 2nd one. You have to keep everything on the same sides of the equals signs when you do it, and put a negative sign around the ENTIRE 2nd equation (that always got me lol).

3x + 7y = 47

- (-4x + 7y = 19)

3x + 7y + 4x -7y = 47 - 19

    7x =  28

    x = 4

Now that you have one variable, all you need to do is plug in the known variable (x) into either original equation.

3 (4) + 7y = 47

12 + 7y = 47

7y = 35

y = 5

Good luck in all your future math problems!

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2