If the problem says “solve for x” then you only Regents specific tip: If the problem says “solve for x” then you only have to find the x-value. In this case, usually the y’s cancel out immediately. If the problem says “solve for y” then usually the x’s will cancel out immediately with little extra work needed to get them to cancel out. Example: Solve the following system of equations for x: 3x + 7y = 17 7x – 7y = 23 This is easy enough that you should be able to do it in your head! If you solve for y then substitute to find x, you’re wasting your time. Also, y turns out to be a decimal value.

THE EQUAL SIGNS MUST LINE UP!!!!!!!!! 2x + 3y = 17 3x = 15 – 4y  rearrange this equation to make it line up with the other equation (add 4y to both sides) This becomes: 2x + 3y = 17  keep both equations written together like this 3x + 4y = 15 after rearranging. Then, when you multiply, work across.

Example: (THIS IS EXACTLY HOW I WANT YOUR WORK TO LOOK!) 2x = 4y -2 5x + 7y = 46 2x = 4y -2  Note: we’re going to subtract 4y from both sides  Note: we’re going to subtract 4y from both sides 5( -2( 2x – 4y = -2 5x + 7y = 46 ) 10x – 20y = -10 -10x – 14y = -92 – 34y = -102 Check: 2x = 4y – 2 2(5) = 4(3) -2 10 = 10 5x + 7y = 46 5(5)+7(3) = 46 25+21 = 46 46 = 46 – 34 – 34 y = 3 2x = 4(3) – 2 2x = 12 – 2 2x = 10 x = 5 ANS: (5,3)

Same Example: I’ll do it a different way though – getting rid of y’s first) 2x = 4y -2 5x + 7y = 46 2x = 4y -2  Note: we’re going to subtract 4y from both sides  Note: we’re going to subtract 4y from both sides 7( 4( 2x – 4y = -2 5x + 7y = 46 ) 14x – 28y = -14 20x + 28y = 184 34x = 170 Check: 2x = 4y – 2 2(5) = 4(3) -2 10 = 10 5x + 7y = 46 5(5)+7(3) = 46 25+21 = 46 46 = 46 34 34 x = 5 2(5) = 4y – 2 10 = 4y -2 12 = 4y 3 = y ANS: (5,3)