What is the ordered pair of x+y<6; y≥ 7x-3?

the question is: Which ordered pair is a solution to x+y<6; y≥ 7x-3?
answer choices are : A. (1,4) B. (3,6) C. (2,5) D. (2,-1)

1 Answer
SCooke
Apr 27, 2018

"A" (1,4) is the only set that satisfies these conditions.

Explanation:

Well, "brute force" can be used by just putting the values into the expressions and seeing which one matches. OR we can solve them as linear equations to find the solution range.
#x + y < 6#
#-7x + y ≥ - 3#

#x + y < 6#
#7x - y <= 3# solve as an equality first, then check the condition.

#x + y = 6#
#7x - y = 3# add the two

#8x = 9# ; #x = 9/8#

#9/8 + y < 6# ; #y < 6 - 9/8# ; #y < 4.875#

CHECK
#7x - y <= 3# ; #7(9/8) - 4.875 <= 3#
#7.875 - 4.875 <= 3# ; #3 <= 3# CORRECT

#x + 4.875 < 6# ; #x < 1.125#
SO, the solution must have a y-value less than 4.875 and an x-value less than 1.125.
"A" (1,4) is the only set that satisfies these conditions.

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