Solve the following simultaneouse equation. 3x+y=1 and x²+y²=5

x=2/5,      y=11/5

or x=−1y = 2

Step-by-step explanation:

Substitute y=3x+1 in x2+y2=5 to obtain

x2+(3x+1)2=5    ⇒    10x2+6x−4=0

Hence

5x2+3x−2=0    ⇒    5x2+5x−2x−2=0    ⇒5x(x+1)−2(x+1)= 0   ⇒ (5x−2)(x+1)=0

Hence

either

x=2/5, y=3×2/5+1=11/5

or x=−1, y=3×(−1) +1 = −2

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

(x+3)(x+7)

step-by-step explanation: