4 Old MacDonald has a paddock in the shape $O A B C$. When drawn on Cartesian axes, the paddock is bounded by the $y$-axis, the $x$-axis and the lines with the equations \[ y=3 x+1 \text { and } y=-5 x+15 \] a Find the coordinates of $A$. \begin{tabular}{l|l} $y=3 x+1$ & $3 x+1=-5 x+15$ \\ $y=-5 x+15$ & $8 x=14$ \end{tabular} b Find the coordinates of $C$.

Step 1 ：\(A\) is the intersection of \(y = 3x + 1\) and \(y = -5x + 15\). We solve the system of equations:

Step 2 ：\(3x + 1 = -5x + 15\)

Step 3 ：\(8x = 14\)

Step 4 ：\(x = \frac{7}{4}\)

Step 5 ：Substitute \(x\) back into either equation to find \(y\):

Step 6 ：\(y = 3\left(\frac{7}{4}\right) + 1\)

Step 7 ：\(y = \frac{15}{4}\)

Step 8 ：So, \(A\) has coordinates \(\boxed{\left(\frac{7}{4}, \frac{15}{4}\right)}\)

Step 9 ：\(C\) is the intersection of \(y = -5x + 15\) and the \(x\)-axis. When a point is on the \(x\)-axis, its \(y\)-coordinate is 0:

Step 10 ：\(0 = -5x + 15\)

Step 11 ：\(5x = 15\)

Step 12 ：\(x = 3\)

Step 13 ：So, \(C\) has coordinates \(\boxed{(3, 0)}\)