Solve algebraically the following system of equations: 4x + 5y = -3; 6x - 2y = 5

To solve these algebraically, we need to eliminate one of the two variables (either x or y) and solve for the remaining variable. We then substitute the answer found into one of the two given equations to find the other answer.So, first to eliminate one of the variables, here we shall eliminate y, we need to scale the two equations so that the multiples of y are the same in both. To do this, we multiply the first equation by 2 to get 8x + 10y = -6 and the second by 5 to get 30x - 10y = 25. (Note: remember to do the same to both sides of the equation) We then add the two equations together, left side to left side and right to right, to get 8x + 10y + 30x - 10y = -6 + 25, which reduces down to 38x = 19, and so we have found that x = 1/2. (Note: don't forget the minus signs!). Now that we have one answer, we simply substitute this into one of the equations to find y, as so: 4(1/2) + 5y = -3, so 2 + 5y = -3, so 5y = -5, and y = -1.