Solve the simultaneous equations to find x and y. 4X=8Y+24; 7Y=23-2X

To solve these simultaneous equations I will use the substitution method. This method consists of finding out the value of one of the variables (X and Y) and then substituting this value into the other equation. This will allow us to find a numerical value for the variable. It will become clearer as we walk through the question. We take the first equation: 4X=8Y+24. We then divide both sides by 4 so we can get a value of X. We are trying to alter the equation so we get just X on one side of the equals sign. We are then left with X=2Y+6. Now we have a value of X from one equation we can substitute it into the other equation in place of X. This leaves us with: 7Y=15-2(2Y+6). We can expand by multiplying the bracket by 2. This gives us: 7Y=23-4Y-12, which we can cancel to: 7Y=11-4Y if we add 4Y to both sides: 11Y=11. We then can divide both sides by 11 to find the value of Y, which is 1. The aim of adding 4Y to both sides is we wish to separate constants (normal numbers) and variables (X and Y) onto different sides of the equals sign. This helps us find Y. Once we have the numerical value of one variable we can find the other by substituting that value into either equation: 4X=8(1)+24 this cancels down to: 4X=32. If we divide both sides by 4 we can find X. In this example X=8. We now have the values that solve for those simultaneous equations.