# Dynamic update of displayed quantities on a Plot within manipulate

I'll admit that I only skimmed some other threads about this. They seem rather complicated in contrast to my simple problem. I have two lines in space defined by a two-by-two coefficient matrix. I intend to manipulate on a single entry, say the (1,2)-element. In the static case I worked to display the intersection point, between the two lines, on the graph. The goal is to watch the point of intersection change as the parameter changes. My code:

a = 1;
f = 3;
c = 2;
d = 1;
g = -1;

Line1 :=  a  x + b y ;
Line2 :=  c x + d y;
IntersectionPoint := Solve[Line1 == f && Line2 == g, {x, y}]
xIntersection := x /. IntersectionPoint[[1]][[1]]
yIntersection := y /. IntersectionPoint[[1]][[2]]

Manipulate[ContourPlot[{a x + b y == f, c x + d y == g}, {x, -5, 5}, {y, -5, 5},
PlotLegends -> True, Axes -> True,
AxesLabel -> {x, y},
Epilog -> {{Text[StringJoin["Point of Intersection:", "
(x,y)=(", ToString[ N[xIntersection]],
",", ToString[N[yIntersection]] , ")"],
Scaled[{.62, .8}]]}}], {b, -10, 10}]

• Update: I posted before I asked my question. If you run the above code then you will see a symbolic result displayed on the screen that does not take into account the current value of the manipulated parameter 'b'. I would like the numerical value of the intersection point displayed through the manipulated values.
– user32569
Aug 23, 2015 at 18:02
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• What is the problem here? Can you spell out what does work, and what doesn't? What would you like help with? Aug 23, 2015 at 18:53

Manipulate[{