7r-3s=18
3r+7s=16
Solve by the elimination method, please.
7r-3s=18
3r+7s=16
21r -9s =54
-21r-49s=-112
-58s=-58
solve for s, then put that back into one of the equations to solve for r
solve by elimination
7r-3s=-17
3r+7s=59
To solve this system of equations using the elimination method, we need to eliminate one of the variables by multiplying one of the equations by a suitable constant so that the coefficients of one of the variables in both equations become equal in magnitude but opposite in sign.
Let's eliminate the variable 'r' in this case:
1. Multiply the first equation by 3 and the second equation by 7 to make the coefficients of 'r' in both equations equal:
Equation 1: 3*(7r - 3s) = 3*18 => 21r - 9s = 54
Equation 2: 7*(3r + 7s) = 7*16 => 21r + 49s = 112
2. Now, subtract equation 2 from equation 1 to eliminate 'r':
(21r - 9s) - (21r + 49s) = 54 - 112
21r - 9s - 21r - 49s = -58
-9s - 49s = -58
-58s = -58
3. Simplify the equation:
-58s = -58
4. Divide both sides of the equation by -58 to solve for 's':
s = -58 / -58
s = 1
5. Substitute the value of 's' back into one of the original equations (let's use the first equation) and solve for 'r':
7r - 3(1) = 18
7r - 3 = 18
7r = 18 + 3
7r = 21
r = 21 / 7
r = 3
Hence, the solution to the system of equations is r = 3 and s = 1.