Solve the simultaneous equation: 2x + y = 5, 3x + 4y = 10

So the aim of simultaneous equations like this, are to figure out the value of x and y. The first thing you have to decide is which one to figure out first. You have to make both 'x' values or both 'y' values equal, so the easiest way to decide which, is to see which one requires the least amount of multiplication to get equal values. In this equation, regarding the 'x' values, we'd have to make both of them equal to '6x' (the lowest common denominator) and therefore multiply equation (1) by 3 (2x x 3 = 6x) and equation (2) by 2 (3x x 2 = 6x). However, if we look at the y values, the lowest common denominator is '4y', meaning that we can leave equation (2) as it is, and only have to multiply equation (1) by 4 (y x 4 = 4y). So it would be easier to look at the 'y' values first. So, we know that we have to make the y values equal, and to do this we have to multiply equation (1) by 4. Remember, that whatever you do to one value in the equation, you have to do to all the values in order to make the equation still work. For example, 1+2=3. If we multiply '1' by 2, the equation doesn't hold true anymore: 2+2=3. But, if we multiply all the values by 2, it still makes sense: 2+4=6. Therefore, multiply all the values of equation (1) by 4. This gives us the equation, 8x + 4y = 20, which we'll call equation (3). We then need to combine equation (2) and (3) in a way that gets rid of the 'y' values. The easiest way to decide what sum to do (addition or subtraction) is to look at the sign (+ or -) in front of the 'y' values. Same Sign Subtract (SSS) or Different Sign Add (DSA). Here, both the 'y' values have a '+' in front of them and therefore we subtract (SSS). It doesn't matter which way round you do the sum, as long as it's the same for all values. So, equation (3) minus equation (2), gives us: 5x = 10. By solving this equation, we can see that x = 2. Substituting this value into equation (1), we can see that 2(2) + y = 5 and therefore 4 + y = 5. Therefore, y =1. Make sure to substitute both values into to the other equation to make sure that they're correct: equation (2): 3(2) + 4(1) = 10, so 6 +4 = 10, and you can be certain your answers are correct.