Answer:
x = 5/e
Step-by-step explanation:
ln x- ln 5= -1
We know that ln a - ln b = ln (a/b)
ln x- ln 5= -1
ln(x/5) = -1
Raise each side to the power of e
e^ ln(x/5) = e^-1
We know that e^-1 = 1/e
x/5 = 1/e
Multiply each side by 5
x/5 *5 = 1/e * 5
x = 5/e
x - y = 12 ⇒ 3x - 3y = 36
2x + 3y = 76 ⇒ 2x + 3y = 76
5x = 112
5 5
x = 22.4
x - y = 12
22.4 - y = 12
- 22.4 - 22.4
-y = -10.4
-1 -1
y = 10.4
(x, y) = (22.4, 10.4)
The number 12 belongs to a set of even numbers
So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.
