Solve by the elimination method:

7r-9s=-35
9r+7s=85

(7r-9s)7=(-35) 7

(9r+7s)9=85.9
7(7r-9s)=765
7(7r-9s)=-35.7
9(9r+9s)=765
7(7r-9s)=-245
9.9r+9.7s=765
7.7r-7.9s=-245
81r+63s=765
49r-63s=-245
81r+63s=765
49r-63s=-245
(81r+63s)+(49r-63s)=765.245
49r-63s=-245
1230r=520
49r-63s=-245
130r/130=520/130
49r-63s=-245
r=2^3-1
49r-63s=-245
r=4
49.4-63s=-245
196-63s=-441
63s/63=441/63
s=7^2-1
s=7

No, no, no, no, no, no, no...I have no idea what all that nonsense above is.

7r-9s=-35
9r+7s=85
Multiply the first equation by 7 and the bottom by 9 so that the s's cancel.
49r-63s=-245
81r+63s= 765
130r=520
r=4
Now put r=4 back into any original equation.
9(4)+7s=85
36+7s=85
7s=49
s=7
(4,7)

To solve this system of equations using the elimination method, we want to eliminate one variable by manipulating the equations so that when they are added or subtracted, one variable cancels out.

Let's start by multiplying the first equation by 9 and the second equation by 7 to make the coefficients of r in both equations equal:

(9)(7r - 9s) = (9)(-35)
(7)(9r + 7s) = (7)(85)

Simplifying these equations gives us:

63r - 81s = -315 [Equation 1]
63r + 49s = 595 [Equation 2]

Now let's subtract Equation 1 from Equation 2 to eliminate the r variable:

(63r + 49s) - (63r - 81s) = 595 - (-315)

Simplifying further, we have:

63r + 49s - 63r + 81s = 595 + 315

Combining like terms, we get:

(49s + 81s) = 595 + 315

Simplifying:

130s = 910

To solve for s, we divide both sides of the equation by 130:

s = 910 / 130
s = 7

Now that we have the value of s, we can substitute it back into one of the original equations to solve for r. Let's use the first equation:

7r - 9s = -35

Substituting s = 7, we have:

7r - 9(7) = -35

Simplifying:

7r - 63 = -35

Adding 63 to both sides:

7r = -35 + 63
7r = 28

Dividing both sides by 7:

r = 28 / 7
r = 4

So the solution to the system of equations is r = 4 and s = 7.