Solve the simultaneous equations: 3x + 2y = 4 and 4x + 5y = 17

Step 1: multiply one or both equations so that the 2 equations have the same coefficient for either x or y (pick easier one) 5(3x + 2y) = 5(4) --> 15x + 10y = 20 AND 2(4x + 5y) = 2(17) --> 8x + 10y = 34 | Step 2: subtract one equation from the other 15x + 10y = 20 MINUS 8x + 10y = 34 --> (15x + 10y) - (8x + 10y) = 20 - 34 --> 7x = -14 | Step 3: solve the new equation 7x = -14 --> x = -2 | Step 4: substitute x = -2 into either one of our very first equations and solve to find y 3(-2) + 2y = 4 --> -6 + 2y = 4 --> 2y = 10 --> y = 5 | Step 5: check that our values for x and y are correct by substituting our values into the other initial equation