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Answer 1

To determine the number of solutions for the given system of equations, we can solve it using different methods.

First, let's solve the system of equations:

Equation 1: y = -2x + 12

Equation 2: 4y + x - 20 = 0

Substituting the value of y from Equation 1 into Equation 2:

4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4

Substituting the value of x into Equation 1:

y = -2(4) + 12
y = -8 + 12
y = 4

So we have found the solution x = 4, y = 4.

Since the two equations intersect at a single point, the system of equations has one solution.

Therefore, the correct answer is: One solution.