Question

solve system of equation
r-s=-3
r+s+9

Answer 1

Lets start by separating the terms and work them out in groups.
The first one we will do is:
3(r + 4)
When you are multiplying by numbers or variable in parentheses, you distribute the number into the parentheses like this:
(3*r + 3*4)
this simplifies to:
3r + 12

next
2(r - 3)
distribute like i did earlier:
(2*r - 2*3)
simplify:
2r - 6

and finally, the last one on the other side of the equation:
2(2r - 3)
distribute again:
2*2r - 2*3
simplify:
4r - 6

So lets put Humpty back together again and we get:
3r + 12 + 2r - 6 = 4r - 6

remember that subtracting a number is the same as adding the complete opposite of that number, so now our equation becomes:
3r + 12 + 2r + (-6) = 4r + (-6)
Now we combine like terms:
3r + 12 + 2r + (-6) = 4r + (-6)
5r + 12 + (-6) = 4r + (-6)
5r + 6 = 4r + (-6)
now lets subtract 4r from both sides of the equation:
5r + 6 - 4r = 4r + (-6) - 4r
r + 6 = (-6)
Note that the 4r's on the right side of the equation cancel each other out.

Now lets subtract 6 from both sides of the equation:
r + 6 - 6 = (-6) - 6
r = (-6) - 6
r = (-12)

Hope that helps :-)

Answer 2

Add the two equations to get


r-s=-3
r+s=9
-------
2r+0s = 6

So 2r = 6

Solve that for r

Then use the solution for r to find the solution for s