4. What is the y-coordinate of the solution of the following system? ) 3x+3y=0 4x-y=5

To find the \( y \)-coordinate of the solution to the system of equations, we can use either the substitution method or the elimination method. Here, we'll use the elimination method.<br /><br />The given system of equations is:<br />\[<br />\begin{cases}<br />3x + 3y = 0 \\<br />4x - y = 5<br />\end{cases}<br />\]<br /><br />First, let's simplify the first equation by dividing everything by 3:<br />\[<br />x + y = 0<br />\]<br /><br />Now our system looks like this:<br />\[<br />\begin{cases}<br />x + y = 0 \\<br />4x - y = 5<br />\end{cases}<br />\]<br /><br />Next, we add the two equations together to eliminate \( y \):<br />\[<br />(x + y) + (4x - y) = 0 + 5<br />\]<br />\[<br />x + y + 4x - y = 5<br />\]<br />\[<br />5x = 5<br />\]<br />\[<br />x = 1<br />\]<br /><br />Now that we have \( x = 1 \), we substitute it back into the simplified first equation to find \( y \):<br />\[<br />x + y = 0<br />\]<br />\[<br />1 + y = 0<br />\]<br />\[<br />y = -1<br />\]<br /><br />Therefore, the \( y \)-coordinate of the solution is \( -1 \).