A waitress sold 15 ribeye steak dinners and 18 grilled salmon​ dinners, totaling ​$559.81 on a particular day. Another day she sold 19 ribeye steak dinners and 9 grilled salmon​ dinners, totaling ​583.66. How much did each type of dinner​ cost?

Let  the steaks = X and the salmon = y.Set up two equations: 15x + 18y = 559.8119x + 9y = 583.66Now using the elimination method:Multiply the second equation by -2, then add the equations together. (15x+18y=559.81) −2(19x+9y=583.66) Becomes: 15x+18y=559.81 −38x−18y=−1167.32 Add these equations to eliminate y: −23x=−607.51 Divide both sides by -23 to solve for x: x= -607.51 = -23 = 26.413478Now you have the cost for a steak. To solve for the cost of the salmon, replace x with the value in the first equation and solve for y.15(26.413478) + 18y = 559.91396.202174 + 18y = 559.81Subtract 396.202174 from both sides:18y = 163.607826Divide both sides by 18:y = 163.607826 / 18y = 9.089324Round both x and Y to the nearest cent:X (Steaks) =$26.41 Y (Salmon) = $9.09