I need the formula for the following?

5x +3y = -7 -----> equation 1
7x -3y = 55 -----> equation 2

By elimination,

(5x + 3y) + (7x - 3y) = -7 +55
12x = 48
x = 48/12
x = 4 -----> equation 3

Substitute x = 4 (equation 3) into equation 2

7x - 3y = 55
7(4) - 3y = 55
28 - 3y = 55
-3y = 55 -28
-3y = 27
y = -27/3
y = -9

therefore, x = 4 and y = -9

add two numbers together
= x +y
= 4 +(-9)
= 4 -9
= -5

You have 2 equations and 2 unknowns.
Use elimination method by adding the two equations together to eliminate the y:
(5x + 3y = -7)
+ (7x - 3y = 55)
______________
(12x = 48)
x = 4
Plug x into one of the two original equation:
(lets pick the first equation)
5(4) + 3y = -7
20 + 3y = -7
3y = -27
y = -9

so the sum of the two number x and y = 4 + -9 = -5

For this kind of problem, you can set it up like so:
5x + 3y = -7
(+)7x - 3y = 55

Then you go ahead and add vertically, (meaning, add the x's together, add the y's, and add the numbers), so you get:

12x = 48
x=4

Then go ahead and plug in the value you got for x into one of the equations to find y.

5x + 3y = -7
5(4) + 3y = -7
3y = -27
y = 9

*Note, the reason this works is because the y's cancel when you add the 2 equations together. If the 2nd equation had been 7x + 4y = 55, then what you'd have to do is:

(4)(5x + 3y = -7)
(-3)(7x + 4y = 55)

And then you're equations would be:

20x + 12y = -28
-21x - 12y = -165

The 12y's would cancel, and you can proceed to solve it like you did before.

X=4
Y=-9

Answer=-5

5x + 3y = -7 Eq. (1)
7x - 3y = 55 Eq. (2)
---add----------------
12x = 48
x = 48/12 = 4

35x + 21y = -49 Eq. (1) x 7
35x - 15y = 275 Eq. (2) x 5
----subtract-------------------
36y = -324
y = -324/36 = -9

(x, y) = (4, -9)

Add the two equations together...
This gives
5x+7x+3y-3y=55-7
This cancels the y values
12x=48
x=4
Sub this back into an equation...
5(4)+3y= -7
20+3y= -7
3y = -27
y= -9
y+x = -3

x=4, y=-9