Solve the simultaneous equations 6x - 27 = 15 and 4x + 3y = -3.

Initially we have two unknown variables, so we want to eliminate one of the variables (x) to solve for the other (y). The LCM of 6 and 4 is 12, so multiply each equation such that the coefficient of x is 12:2*(6x - 2y = 15) --> 12x - 4y = 303*(4x + 3y = -3) --> 12x + 9y = -9Subtracting equation 2 from equation 1 eliminates the variable x and gives y = -3. This value is then substituted back into one of the original equations to find the value of x. For example:6x - 2(-3) = 156x = 9x = 1.5Therefore, we have our two solutions whereby x = 1.5, y = -3.