Solve this simultaneous equation: 5x+6y=3 and 2x-3y=12.

Firstly, I will provide a mark scheme and then a full explanation underneath. 5x+6y=3. (1) 2x-3y=12. (2). (5x+6y=3)+(2(2x-3y=12)). (5x+6y=12)+ (4x-6y=24). 9x=27. x=3. Put x is (1) 5(3)+6y=3=15+6y=3. 6y=-12. y=-2. Check in (2). 2(3)-3(-2)=12. 12=12. Therefore x=3 and y=-2. 5x+6y=3. 2x-3y=12. Now a full explanation: Treat 5x+6y=3 as No. 1 equation. Treat 2x-3y=12 as No.2 equation. Therefore, 5x+6y=3 (1) and 2x-3y=12 (2). (There needs to be something equal about these two equations. TOP TIP: REMEMBER WHEN DOUBLING BOTH THINGS EITHER SIDE OF THE '=', IT STILL MEANS THE SAME THING :) YOU CAN PRETTY MUCH DO ANYTHING TO AN EQUATION AS LONG AS YOU DO THE SAME THING FOR EITHER SIDE OF THE '=' SIGN). In this case, an easy way to make the equation equal and able to manipulate would be to multiply (2) by 2. Therefore,  2(2x-3y)= 24. This equals 4x-6y=24. Now as the y's are equal you can 'simultaneously' solve them. Effectively, we need to get rid of the y's. Therefore add (5x+6y=3) and (4x-6y=24). This gives us 9x=27. (as 5+4 =9, 6-6=0 and 3+24=27.) Therefore, x=3. Now put x= back into one of the equation, for example in (1). This gives 5(3)+6y=3. Therefore 15+6y=3. (take 15 from both sides). 6y=3-15. . 6y=-12. (divide both sides by 6). y=-2. Therefore x=3. y=-2. Feel free to check your results using (2) to make sure your answers right. Therefore, 2(3)-3(-2)=12. This gives 6--6=12. 12=12. Therefore, we have got the right answer.