Solve the Simultaneous equations 4x - y = 8 and x + y = 12

One basic method used here, when you have an equation and you add, subtract, multiply or divide one side of the equation from the equal sign, you must add, subtract, multiply or divide by the same value on the other side of the equal sign. (Give pupil basic example)Label equations [1] 4x - y = 8 and [2] x + y = 12Rearrange [1] and [2] to make them easier to solve by adding and subtracting numbers to both sides of the equals sign[1] 4x - y = 8 becomes 4x = 8 + y (added y to both sides) which then becomes y = 4x - 8 (subtracted 8)[2] x + y = 12 becomes y = 12 - x (subtracted x)Since y = y, we can now make the equations equal to each other as the both equal y. So we get 12 - x = 4x - 8We want the same terms on opposite sides so we want all the x's on one side and the numbers on the other.This gets us 20 = 5x (added x and 8 to both sides)Divide both sides by 5 to get first part of solution... x = 4 (as 20/5 = 4)Plug in x = 4 to either [1] or [2]. [2] looks easier as it just x in that equation. x + y = 12 becomes 4 + y = 12 as x = 4 which then becomes y = 8 when you subtract 4 from both sides.y = 8 is the second part of the solution.You can also check this answer by plugging x = 4 to the other equation we started with [1] to see if it gives us the same answer for y.4x - y = 8 becomes 4*4 - y = 8 = 16 - y becomes -8 = -y which shows y = 8 when both sides are multiplied by -1. So the correct answer is...x = 4 and y = 8