Solving by substitution?

-x-3y=15
2x+7y=-36

now lets call the 1st equation (1).. and the 2nd (2)

from (1) ... -x-3y=15
-x=15+3y (we want a simple "x" to use so we take the "3y" to the other side and change the sign)
now we take the "-1" from the x to the other side to have positive x
so it's... x=15+3y/-1
we solve it.. x= -15-3y.. (so now we found that x=-15-3y)
now we use the equation (2).... 2x+7y=-36
(we use "-15-3y" in place of x) 2(-15-3y)+7y=-36
(we do the multiplication) -30-6y+7y=-36
(add the 2 y's) ... -30+y=-36
take the "-30" to the other side nd change the sign)... y=-36+30
which is -6.. so y=-6
now use the equation for x (x=-15-3y) and use "-6" for y
so.. x=-15-3*-6
we solve it.. x= -15+18= 3

you got... y= -6.. and x=3

now check your answer
-x-3y=15
so -3-3*-6= 15.. which is correct

I'm not that good in explaining things.. I'm only 15.. but hope that helped

good luck

-x-3y= 15
therefore, x= -15-3y

now take the second equation and put x= -15-3y

2(-15-3y) + 7y= -36
-30 -6y +7y =-36
-30 +y=-36
y= -6

and x = -15+18
or x= 3

-x - 3y = 15
2x + 7y = -36

-x - 3y = 15
-x = 15 + 3y
x = -15 - 3y

2x + 7y = -36
2(-15 - 3y) + 7y = -36
-30 - 6y + 7y = -36
-6y + 7y = -36 + 30
y = -6

-x - 3y = 15
-x - 3(-6) = 15
-x - (-18) = 15
-x + 18 = 15
-x = 15 - 18
x = -3/-1
x = 3

∴ x = 3 , y = -6

-x-3y= 15 (1)
2x+7y= -36 (2)
-x=15+3y (1)
x=-15-3y (1)

( sub 1--->2) 2(-15-3y)+7y=-36
-30-6y+7y=-36
y= -36+30
y= -6 (3)

( sub 3--->1) -x-3(-6)=15
-x+18=15
-x=15-18
-x=-3
x=3

therefore x=3, y= -6

x=3

multiple first equation by 2
-2x-6y = 30
add it to second one
y = 30-36 = -6
and put it in first to get x
-2x = 30+6*-6
x = 3

x = - 3y - 15

- 6y - 30 + 7y = - 36
y = - 6

2x - 42 = - 36
2x = 6
x = 3

x = 3 , y = - 6

The 1st poster used elimination!

For substitution:

First solve for one of the variables (using either equation).
In the 1st eq, x=-3y-15. (add x to both sides, subtract 15 from both)
now substitute -3y-15 for x in the 2nd eq.
2(-3y-15)+7y=-36
solve for y
y=-6

now substitute -6 for y in either eq. and solve for x
x=3
EDIT: "However, if I chose to rearrange y, how would I sub it into the equation?" There would be no difference. Exactly the same procedure.