How do I solve the simultaneous equations 2x - y = 3 and 3x + y = 9

First of all you need to spot a way we can add or subtract these two equations together so that we can get rid of one of the terms. This is easily spotted by writing the equations like so:2x - y = 13x + y = 9We can see that as both equations only consist of one y, and because one of them is +y and the other is -y, if we simply add both equations together the y term will disappear ((+y )+ (-y) = 0); we can use brackets to make the calculations simpler, this is especially useful when subtracting and multiplying is also needed to get rid of a term:(2x - y) + (3x + y) = (1) + (9), simplify out the brackets;2x - y + 3x + y = 1 + 9, collect all the terms together;5x = 10, now we simply divide 10 by 5 to get our first result x = 2We can then put this result back into either of our equations to get a value for y (we choose the first equation 2x - y = 1);2x - y = 1, plug in our value for x;2(2) - y = 1, simplify out the brackets and collect like terms;4 - 1 = y, y = 3.Now we have x = 2 and y = 3. We can check that these are correct by putting both of the values into the equation we didn't use (3x + y = 9)3x + y = 9, plug in our values;3(2) + (3) = 9, simplify;9 = 9, so we can see that we have achieved the correct answer.