Solve the following systems of equations using the addition (elimination) method.

5x=20+y
16=3y+4x

x3: 15x=60+3y

- -4x=-16+3y
19x=76
x=4
y=o

To solve the system of equations using the addition (elimination) method, we need to eliminate one variable by adding or subtracting the equations. Let's start by eliminating the variable "x" in the equations.

First, we will write the equations in standard form (ax + by = c) if they are not already in that form.

Given equations:
5x = 20 + y ----(1)
4x + 3y = 16 ----(2)

Now, to eliminate the variable "x," we need to manipulate the equations so that the coefficients of "x" in both equations have the same magnitude but opposite signs. In this case, we can multiply equation (1) by 4 and equation (2) by 5 to achieve this:

4(5x) = 4(20 + y) ---- Multiply equation (1) by 4
5(4x + 3y) = 5(16) ---- Multiply equation (2) by 5

This simplifies the equations to:

20x = 80 + 4y ----(3)
20x + 15y = 80 ----(4)

Now, we can subtract equation (3) from equation (4) to eliminate "x":

20x + 15y - 20x = 80 - 80

This results in:

15y = 0

From this equation, we can deduce that y = 0.

To find the value of "x," we substitute y = 0 into one of the original equations. Let's use equation (1):

5x = 20 + 0
5x = 20
x = 20/5
x = 4

Therefore, the solution to the system of equations is x = 4 and y = 0.