solve by the elimination method:
7r-9s=4
9r+7s=98
multipy the first equation by 7, and the second equation by 9.
Then add the equations
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations.
We have the following system of equations:
Equation 1: 7r - 9s = 4
Equation 2: 9r + 7s = 98
To eliminate one of the variables, let's multiply Equation 1 by 9 and Equation 2 by 7 to make the coefficients of either 'r' or 's' the same:
9 * (7r - 9s) = 9 * 4
7 * (9r + 7s) = 7 * 98
Simplifying these equations, we get:
63r - 81s = 36
63r + 49s = 686
Now, subtract the second equation from the first equation to eliminate 'r':
(63r - 81s) - (63r + 49s) = 36 - 686
Simplifying further, we have:
63r - 81s - 63r - 49s = -650
Combining like terms:
-130s = -650
Divide both sides by -130:
s = (-650) / (-130)
s = 5
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 Equation 1:
7r - 9(5) = 4
Simplifying:
7r - 45 = 4
Add 45 to both sides:
7r = 49
Finally, divide both sides by 7:
r = 7
Therefore, the solution to the system of equations is r = 7 and s = 5.