MotionGenesis: F=ma Software, textbooks, training, consulting. Solving linear algebraic equations
To symbolically solve the equations to the right (which are linear in x and y), type
Variable x, y
Eqn[1] = 2*x + 3*y - sin(t)
Eqn[2] = 4*x + 5*y - cos(t)
Solve( Eqn = 0, x, y )
The response to this Solve command is
-> x = 1.5*cos(t) - 2.5*sin(t)
-> y = 2*sin(t) - cos(t)
 
2*x + 3*y   =   sin(t)  
 
4*x + 5*y   =   cos(t)  
To save input and/or input and output responses, type
Save   SolveSampleLinearEqn.txt       % Saves input (for subsequent re-use).
Save   SolveSampleLinearEqn.html       % Saves input and the program's output responses.

Advanced: To write a MATLABŪ code to numerically solve for x and y for   0 <= t <= 3,   type
Variable x, y
Eqn[1] = 2*x + 3*y - sin(t)
Eqn[2] = 4*x + 5*y - cos(t)
Output t seconds, x meters, y meters
Code Algebraic(Eqn = 0, x, y) [t = 0, 3, 0.5] SolveSampleLinearEqn.m
% FILE: SolveSampleLinearEqn.1
%
%       t              x              y
%   (seconds)      (meters)       (meters)

  0.000000E+00   1.500000E+00  -1.000000E+00 
  5.000000E-01   1.178100E-01   8.126852E-02 
  1.000000E+00  -1.293224E+00   1.142640E+00 
  1.500000E+00  -2.387632E+00   1.924253E+00 
  2.000000E+00  -2.897464E+00   2.234742E+00 
  2.500000E+00  -2.697896E+00   1.998088E+00 
  3.000000E+00  -1.837789E+00   1.272233E+00