Y=-5//3x+25 Y=1//3x+4

<p> 1. To find the point of intersection of the two lines given by the equations \( Y = -\frac{5}{3}x + 25 \) and \( Y = \frac{1}{3}x + 4 \), we set the right-hand sides of these equations equal to each other and solve for \( x \):<br /> \[<br /> -\frac{5}{3}x + 25 = \frac{1}{3}x + 4<br /> \]<br /> <br /> 2. We add \(\frac{5}{3}x\) to both sides of the equation to isolate \( x \) terms on one side:<br /> \[<br /> 25 = \frac{1}{3}x + \frac{5}{3}x + 4<br /> \]<br /> <br /> 3. Combining the \( x \) terms on the right side gives:<br /> \[<br /> 25 = \frac{6}{3}x + 4<br /> \]<br /> <br /> 4. We then subtract 4 from both sides to find:<br /> \[<br /> 21 = \frac{6}{3}x<br /> \]<br /> <br /> 5. Dividing both sides by \(\frac{6}{3}\) (or 2) gives:<br /> \[<br /> x = \frac{21}{2}<br /> \]<br /> <br /> 6. Now that we have found \( x \), we can find \( y \) by substituting \( x = \frac{21}{2} \) into either of the original equations. Using the second equation:<br /> \[<br /> y = \frac{1}{3}\left(\frac{21}{2}\right) + 4<br /> \]<br /> <br /> 7. Simplifying further gives:<br /> \[<br /> y = \frac{7}{2} + 4 = \frac{15}{2}<br /> \]<br /> <br /> 8. Therefore, the point of intersection of the two lines is \( \left(\frac{21}{2}, \frac{15}{2}\right) \). </p>