X+y=14 2x+3y=30
How do I determine which method is used for this and what is it? (Thorough explanation please)

x = -18

y = 4

Step-by-step explanation:

x + y = 4

2x + 3y = 30

You can do any math operation to each side of the equal sign as long as you do the same operation to both sides.

change x + y = 4       to        x = 4 - y  

Now substitute (4 - y) into the second equation, in place of x.

2(4-y) + 3y = 30

multiply the 2(4-y) part:

8 -2y + 3y = 30

simplify:

8 + y = 30

subtract 8 from each side:

y = 22

now substitute the value of y back into the first equation to solve for x:

x + 22 = 4

subtract 22 from both sides:

x = -18

Check:

x + y = 4

22 -18 = 4  

4 = 4       (this checks)

2(-18) + 3(22) = 30

-36 + 66 = 30

30 =30     (this checks also)

PS: you could have solved for y first if you had wanted to. The results would be the same.