Question

Consider the following system of equations: 3x - 5y = 4 and 5x + y = 16. Determine the y-coordinate of the solution of the system:

Answer 1

To determine the y-coordinate of the solution for the system of equations 3x - 5y = 4 and 5x + y = 16, we can solve the system by elimination or substitution.

Let's use substitution to solve this system of equations.

First, let's solve the second equation for y:

5x + y = 16
y = 16 - 5x

Now, substitute this expression for y into the first equation:

3x - 5(16 - 5x) = 4
3x - 80 + 25x = 4
28x - 80 = 4
28x = 84
x = 84/28
x = 3

Now that we have found the value of x, substitute it back into the second equation to find y:

5(3) + y = 16
15 + y = 16
y = 16 - 15
y = 1

Therefore, the solution to the system of equations is x = 3 and y = 1. So, the y-coordinate of the solution is 1.