Solve the simultaneous equations '2X+Y=7' and '3X-Y=8'

In order to solve this question we need to remove one variable, either X or Y. Let us remove X in this case. The coefficents of X are 2 and 3. Their lowest common multiplte is 6. We can therefore get both values of X to be 6 in both equations in order to remove this variable. 

Multipying the first equation by 3 gives us 6X+3Y=21. Multipying the second gives us 6X-2Y=16.

If we subtract the first question from the second, the X variable will cancel and we are left with the following:

3y-(-2y)=21-16 which simplifies to 5y=5. Didiving both sides by 5 gives Y=1

The value of Y being 1 can now be substitued back into either equation to find the value of X. Let us try the first one.

2x+(1)=7. Subtracting 1 from both sides gives 2X=6. Dividing both sides by 2 gives X=3.

Our answer can be checked by substituting the values we obtatined for X and Y into the second original equation.

3(3)-1=8. 8=8. We have therefore solved this question. 

Answered by Arjan P. Maths tutor

9630 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The area of a square is 49cm^2. The perimeter of the square is equal to the circumference of a circle. Work out the radius of the circle. Give your answer to 1 decimal place.


Solve (x + 2)(x+3) = (2x+4)


work out the value of 4a + 2b when a = 4 and b = 3


Jenny has 3 stacks of coins - A B and C. Altogether the coins equal £1.30. Stack B has 3 times as much money has Stack A. Stack C has 2 times as much money as Stack B. How much money is in Pile C?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences