SOLUTION: If 5x+y=19 and x-3y=7,then x+y= (A)-4 (B)-1 (C)3 (D)4 (E)It cannot be determined from the information given. Thank you so much!

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Question 473675: If 5x+y=19 and x-3y=7,then x+y=
(A)-4
(B)-1
(C)3
(D)4
(E)It cannot be determined from the information given.
Thank you so much!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Answer is C.
x + y = 3
your values for x and y are:
x = 4
y = -1
this is derived as follows:
your equations are:
5x + y = 19 (first equation)
x - 3y = 7 (second equation)
multiply both sides of the second equation by 5 to get:
5x + y = 19 (first equation)
5x - 15y = 35 (third equation)
subtract the third equation from the first equation to get:
16y = -16
divide both sides of this equation by 16 to get:
y = -1
substitute for y in the first equation to get:
5x - 1 = 19
add 1 to both sides of this equation to get:
5x = 20
divide both sides of this equation by 4 to get:
x = 4
your solutions are:
x = 4
y = -1
confirm by substituting for x and y in both original equations to get:
5x + y = 19 (first equation) becomes 20 - 1 which equals 19 (good).
x - 3y = 7 (second equation) becomes 4 - (-3) = 4 + 3 = 7 (also good).
solutions are good.
x + y = 4 - 1 = 3
that's selection C.