2*x + 3*y = sin(t)
     4*x + t*y = cos(t)

To symbolically solve the previous set of linear equations for x and y, type

Variable  x, y
Zero[1] = 2*x +  3*y  -  sin(t)
Zero[2] = 4*x +  5*y  -  cos(t)
Solve( Zero, x, y )

The response to this Solve command is

->  x = 1.5*cos(t) - 2.5*sin(t)
->  y = 2*sin(t) - cos(t)

To save input (for subsequent re-use) and/or input and output responses, type
Save   SolveSampleLinearEqn.txt
Save   SolveSampleLinearEqn.all