SOLUTION: I need help setting up this problem. The sum of a certain number and a second number is 21. The second number minus the first number is -57. Use a system of two equations wit

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Question 243094: I need help setting up this problem.
The sum of a certain number and a second number is 21.
The second number minus the first number is -57.
Use a system of two equations with two variables to find the numbers.
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need help setting up this problem.
The sum of a certain number and a second number is 21.
The second number minus the first number is -57.
---------------------------
Equations:
x + y = 21
x - y = -57
--------------------------
Add the two equations and solve for "x":
2x = -36
x = -18
----------------------------------
Since x + y = 21
-18 + y = 21
y = 39
===============
Cheers,
Stan H.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 21:
x + y = 21
This means we can show y = 21 - x.
...
The second number minus the first number is -57.
y - x = -57
...
Substituting 21-x for y, we have
21-x -x = -57
21 - 2x = -57
Adding 2x to both sides
21 = -57 +2x
Adding 57 to both sides
21 + 57 = 2x
78 = 2x
Dividing by 2
39 = x
...
x + y = 21
x = 39
29 + y = 21
So, y = -18
...
Checking our work, does the second number minus the first number = -57?
-18 -39 = -57.
Done.