Solve the system:

p-3q=-1
-5p+16q=5

a. (2,1)
b.(3,3)
c. (-1,0)
d.(5,2)

Well, solving this system is no laughing matter, but I'll do my best to bring a little humor into it!

Let's start by solving the system using the Elimination Method. We'll eliminate the "p" variable first.

To eliminate "p," let's multiply the first equation by 5 and the second equation by 1:

5(p - 3q) = 5(-1)
-5p + 16q = 5

Simplifying, we get:

5p - 15q = -5
-5p + 16q = 5

Now, let's add the two equations together:

(5p - 15q) + (-5p + 16q) = -5 + 5

Now, doing some quick math, we can eliminate the "p" variable:

p and -p cancel each other out!

So, we're left with:

q = 0

Now, substitute the value of q back into the first equation:

p - 3(0) = -1

Simplifying, we find:

p = -1

So, the solution to the system is (-1, 0).

Therefore, the correct answer is c. (-1, 0).

I hope my humorous explanation makes the process a little more enjoyable for you!

To solve the system of equations:

1. Start by solving one of the equations for one variable in terms of the other.
From the first equation: p - 3q = -1, rearrange it to get p = 3q - 1.

2. Substitute this expression for p in the second equation.
Replace p in the second equation (-5p + 16q = 5) with 3q - 1:
-5(3q - 1) + 16q = 5

3. Simplify and solve for q.
-15q + 5 + 16q = 5
q + 5 = 5
q = 5 - 5
q = 0

4. Substitute the value of q into the first equation to find p.
p - 3(0) = -1
p = -1

5. The solution to the system of equations is (p, q) = (-1, 0).

Therefore, the correct answer is c. (-1, 0).

To solve the given system of equations, we can use the method of elimination or substitution. Let's solve it using the elimination method.

Step 1: Multiply the first equation by 5 and the second equation by 1 to make the coefficients of p or q opposite in sign:

5(p - 3q) = 5(-1) (First equation x 5)
-5p + 16q = 5 (Second equation x 1)

Simplifying, we get:
5p - 15q = -5
-5p + 16q = 5

Step 2: Add the two equations together to eliminate the p variable:
(5p - 15q) + (-5p + 16q) = -5 + 5

Simplifying, we get:
p + q = 0 (Equation 3)

Step 3: Solve Equation 3 for p or q:
p = -q

Step 4: Substitute the value of p from Equation 3 into any of the original equations. Let's use the first equation:
p - 3q = -1

Substituting -q for p, we get:
(-q) - 3q = -1

Simplifying, we get:
-4q = -1

Step 5: Solve for q:
q = (-1) / (-4)
q = 1/4

Step 6: Substitute the value of q back into Equation 3 to find p:
p = -q
p = -(1/4)
p = -1/4

Therefore, the solution to the given system of equations is (p, q) = (-1/4, 1/4).

None of the answer choices provided matches this solution, so it seems there may be an error in the given system of equations or answer choices. Double-check the problem statement for accuracy.

1st times 5 ... 5p - 15q = -5

add to 2nd to eliminate p
... q = 0