Select the ordered pair from the choices below that is a solution to the following system of equations:

4y = x - 13
2x + 16y = 20

Write 1st Eq in STD form:

x - 4y = 13
2x + 16y = 20
Multiply 1st Eq by -2:
-2x + 8y = -26
2x + 16y = 20
Add the 2 Eq:
24y = -6
y = -1/4
Substitute -1/4 for y in the 1st Eq
and solve for x:
x - 4(-1/4) 13
x = 12.

(12 , -1/4).

3x + 4y = -12

6x + 8y =-16

To find the ordered pair that is a solution to the system of equations, we can substitute the values of the variables into each equation and check if both equations are satisfied.

Let's solve the system of equations step by step:

1) 4y = x - 13

Rearranging this equation, we get:
x = 4y + 13

2) 2x + 16y = 20

Substituting the value of x from equation 1 into equation 2:
2(4y + 13) + 16y = 20
8y + 26 + 16y = 20
24y + 26 = 20
24y = -6
y = -6/24
y = -1/4

Substituting the value of y back into equation 1 to find x:
x = 4(-1/4) + 13
x = -1 + 13
x = 12

Therefore, the solution to the system of equations is (x, y) = (12, -1/4).

Now we can select the ordered pair from the choices provided that matches the solution (12, -1/4).