Both linear functions will intersect at the same point, meaning, the x y coordinates are the same. So you have to equate both equations and clear the value of x:
[tex]\begin{gathered} 3x+4=-2x+1 \\ 3x+2x=1-4 \\ 5x=-3 \\ x=\frac{-3}{5} \end{gathered}[/tex]Now using either function you have to calculate the value of the corresponding y-coordinate, for explanation purposes I'll do it with both:
[tex]\begin{gathered} y=3x+4 \\ y=3\cdot(\frac{-3}{5})+4=\frac{11}{5} \end{gathered}[/tex][tex]\begin{gathered} y=-2x+1 \\ y=-2(\frac{-3}{5})+1=\frac{11}{5} \end{gathered}[/tex]As you see, using either function to calculate the y-coordinate is the same.
The functions intersect in point (-3/5, 11/5)
