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 $A$.

Answer

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Answer

$\boxed{\text{The coordinates of point A are }\left(\frac{7}{4}, \frac{25}{4}\right)}$

Steps

Step 1 ：Find the intersection of the two lines $y = 3x + 1$ and $y = -5x + 15$.

Step 2 ：Set the two equations equal to each other: $3x + 1 = -5x + 15$.

Step 3 ：Solve for x: $8x = 14$ and $x = \frac{7}{4}$.

Step 4 ：Substitute the value of x back into either equation to find the value of y: $y = 3\left(\frac{7}{4}\right) + 1$ and $y = \frac{25}{4}$.

Step 5 ：$\boxed{\text{The coordinates of point A are }\left(\frac{7}{4}, \frac{25}{4}\right)}$