Answer:
[tex](3\ ,\ \frac{17}{4})[/tex]
Step-by-step explanation:
- To find the intersection point you need to set the two equations equal to each other and solve for x .
here is how to do it :
[tex]$\begin{aligned} & -\frac{2}{3} x+\frac{9}{4}=\frac{7}{5} x+\frac{169}{20} \\ & \Leftrightarrow-\frac{2}{3} x-\frac{7}{5} x=\frac{169}{20}-\frac{9}{4} \\ & \Leftrightarrow \frac{-10 x-21 x}{15}=\frac{169-45}{20} \\ & \Leftrightarrow-\frac{31}{15} x=\frac{124}{20} \\ & \Leftrightarrow x=\frac{124}{20} \times\left(-\frac{15}{31}\right) \\ & \Leftrightarrow x=-\frac{1860}{620} \\ & \Leftrightarrow x=-3\end{aligned}$[/tex]
- Now, you can plug it back into either of the original equations to find y.
let’s use g(x) :
[tex]$\begin{aligned} g(-3) & =-\frac{2}{3} \times(-3)+\frac{9}{4} \\ & =2+\frac{9}{4} \\ & =\frac{8+9}{4} \\ & =\frac{17}{4} \\ & =4.25\end{aligned}$[/tex]
Therefore, the coordinates of the intersection points are :
[tex](3\ ,\ \frac{17}{4})[/tex]
