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How do I build an equation with an integer and solve it by the addition/subtraction method.

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This will be for a 2 varriables:  x and y

equations created could be:

  2x  -  3y  =  7

  3x  + y   =  16

You take the two equations and you add them together, keeping the varriables and constants lined up in matching columns (the x's are all in one column, the y's in another, the constants in yet another).

Next, you want to be able to cancel out, via addition, one of the two varriables. Therefore, you need one varriable to be positive, one to be negative. In this example y already has one positive and one negative, so we will use it. Then, you need to make sure the varriables coefficients are the same so that when you add them together you will get a zero and get rid of that varriable. We need to multiply the 2nd equation by 3 to get the proper number.

2x - 3y = 7

(3)(3x + y = 16)   -->   9x  +  3y  =  48

Re-line up the two equations (the original 1st and altered 2nd) so you can clearly see the addition:

     2x  -  3y  =  7

+   9x + 3y  =  48

    11x +  0  =  55

Now solve for remaining varriable, x in this case:

   x  =  5

Plug this answer back into one of your original two equations and solve for y:

3x + y = 16

3(5)  +  y  =  16

15  +  y  =  16

y  =  1


I appreciate the feedback, thank you