Solve by the elimination method.
5r-7s=-37
7r+5s=37
What is the solution of the system? Type an ordered pair.
Multiply equation 1 by -7.
Multiply equation 2 by 5.
Then add the two resulting equations. That will eliminate r. Then solve for s.
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we'll eliminate the variable "s".
First, let's multiply the first equation by 5 and the second equation by 7 to make the coefficients of "s" in both equations equal:
Equation 1: 5r - 7s = -37 (multiply by 5)
Equation 2: 7r + 5s = 37 (multiply by 7)
Now, we have:
25r - 35s = -185
49r + 35s = 259
Add the two equations together:
(25r - 35s) + (49r + 35s) = -185 + 259
25r + 49r = 74r
-35s + 35s = 0
74r + 0 = 74r
Now, we have the equation:
74r = 74
Divide both sides by 74 to solve for "r":
r = 1
Next, substitute the value of r back into one of the original equations. Let's use the first equation:
5r - 7s = -37
Substituting r = 1:
5(1) - 7s = -37
5 - 7s = -37
Now, solve for "s":
-7s = -37 - 5
-7s = -42
s = (-42)/(-7)
s = 6
So, the solution to the system of equations is r = 1 and s = 6. Therefore, the ordered pair solution is (1, 6).