Point at which they intersect is going to have a single y value and a single x value. So at that point, the x and y values are equal:
[tex]y=x^{2}-3 \\
y=3x-4 \\
x^{2}-3=3x-4 \\
x^{2}-3x+1=0 \\
x= \frac{-b± \sqrt{b^{2}-4ac} }{2a} \\
x= \frac{3± \sqrt{9-4} }{2} \\
x= \frac{3± \sqrt{5} }{2} \\
x=2.62, 0.38
[/tex]
So the lines intersect at two x values, 2.62 and 0.38. Now plug them into either equation to find the y values:
[tex]y=3(2.62)-4 \\
y=3.86 [/tex]
[tex]y=3(0.38)-4 \\
y=-2.86[/tex]
So the lines intersect at (2.62,3.86) and (0.38,-2.86)
