Yes, modelica can solve linear equations. But to solve linear equations, the number of unknowns should be equal to the number of equations. In your model x and y are the unknown variables. And "y = a*x +b" is the only equation. So there are two unknowns and only one equation. You should either define one of the two unknown variables or give another equation.
for eg:


model Linear

parameter Real a=2;
parameter Real b=1;

parameter Real y = 9;                 
Real x;

equation

y=a*x + b;


end Linear;
or


model Linear

parameter Real a=2;
parameter Real b=1;

Real y;
Real x;

equation

y=a*x + b;
y = b*x + a;


end Linear;

I appreciate your feedback, however I am looking to plot the evolution of y over values of x from 0 to 10 for example (y=f(x)) and not just solve the equation. So I should probably define the range of values for x. Is that doable ?

Maybe like that:

model linearEquation

  parameter Real a=2;

  parameter Real b=1; 

  Real x = time;

  Real y;

equation

  y = a*x+b;

  annotation(experiment(StopTime = 10));

end linearEquation

so long.
Willi

What if I need the variable 'x' to be independent of time ?

But on what should the rising depend on?

You can have an input:

model linearEquation

  parameter Real a=2;

  parameter Real b=1;

  input Real u;

  Real x(start=0);

  Real y;

equation

   x = u;

   y = a*x+b;

   annotation(experiment(StopTime = 10));

end linearEquation 

Or depending on time in a different order:

model linearEquation

  parameter Real a=2;

  parameter Real b=1;

  Real x(start=0);

  Real y;

equation

   der(x) = if x>=10 then 0 else 1;

  y = a*x+b;

  annotation(experiment(StopTime = 10));

end linearEquation 

so long.
Willi