SOLUTION: solve the system of equations 2r + 2s = 50 and 2r

SOLUTION: solve the system of equations 2r + 2s = 50 and 2r - s = 17

Question 320954: solve the system of equations 2r + 2s = 50 and 2r - s = 17
Answer by Sunny Day(15) (Show Source): You can put this solution on YOUR website!
Solving here means finding the values of 'r' and 's'. For this we need to eliminate one of the variables for which we have to take the variable with the same coefficient (wihtout the signs) in both equations. In this case, 'r' has the coefficient 2 in both (1) and (2). Hence 'r' can be eliminated by subtracting (2) from (1).
2r + 2s = 50 --------- (1)
2r - s = 17 --------- (2)
_______________________________
(1) - (2) ------> 2r + 2s - (2r - s) = 50 - 17
2r + 2s - 2r + s = 33
3s = 33 (since 2r - 2r = 0)

s = 33/3 =11

now, put this value in (1) to get r.
2r + 2X11 = 50
2r + 22 = 50
2r = 50 - 22 = 28
r = 28/2 = 14
So r = 14 and s = 11 is the solution

Cross check: substitute these values of r and s in (2).
ie. 2X14 - 11 = 28 - 11 = 17, which is the given value. hence the solution is verified

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