Given the equations of the lines as follows:
[tex]\begin{gathered} f\mleft(x\mright)=3x-1 \\ g\mleft(x\mright)=-2x+3 \end{gathered}[/tex]We will find the point of intersection between the lines
The condition of the intersection is f(x) = g(x)
so, we can write the following equation:
[tex]3x-1=-2x+3[/tex]Solve the equation to find x, combine the like terms:
[tex]\begin{gathered} 3x+2x=3+1 \\ 5x=4 \\ x=\frac{4}{5}=0.8 \end{gathered}[/tex]Substitute with x into the first equation to find the coordinates of y:
[tex]y=3\cdot0.8-1=2.4-1=1.4[/tex]So, the answer will be the point of intersection will be:
[tex](x,y)=(0.8,1.4)[/tex]