The graphs of #Ax + By=7# and #Ax - By=9# intersect at (4, -1). What is the value of #A# and #B#?

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Answer 1 · 2017-12-05T01:54:33

#A = 2#
#B = 1#

Given:

#Ax + By=7" [1]"#
#Ax - By=9" [2]"#

Substitute 4 for x and -1 for y in both equations:

#4A - B=7" [1.1]"#
#4A + B=9" [2.1]"#

Add equation [1.1] to equation [2.1]:

#4A+4A - B+ B=7+9#

Combine like terms:

#8A = 16#

#A = 2#

Substitute 2 for A in equation [2.1] and then solve for B:

#4(2) + B=9#

#B = 1#

Check:

#2(4) + 1(-1) = 7#
#2(4) - 1(-1) = 9

#7 = 7#
#9 = 9#

This checks.