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.