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

  • Google+ icon
  • LinkedIn icon
  • 911 views

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. 

Arjan P. 11 Plus Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor,...

About the author

is an online GCSE Maths tutor with MyTutor studying at LSE University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok