Final answer:
To solve the given system of equations, we can use the method of elimination. After eliminating the variable y, we find that x = 16/3 and y = 0, which gives us one solution. Therefore, the answer is One Solution.
Step-by-step explanation:
The given system of equations is as follows:
3x + 8y = 16
6x + 3y = 30
2x + 3y = 5
To solve this system, we can use the method of elimination. We'll eliminate the variable y by multiplying the equations. We can multiply the first equation by 3 and the second equation by 8 in order to get the same coefficients for y:
9x + 24y = 48
48x + 24y = 240
We can subtract the two equations to eliminate y:
(48x + 24y) - (9x + 24y) = 240 - 48
Simplifying this, we get:
39x = 192
Dividing by 39, we find that x = 192/39 = 16/3.
Now, substituting this value of x into any of the original equations, we can solve for y. Let's substitute it into the first equation:
3(16/3) + 8y = 16
16 + 8y = 16
8y = 0
y = 0
So, the solution to the system of equations is x = 16/3 and y = 0.
Since there is only one solution to the system, the answer is One Solution.