How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x-5y= -17 and -2x+y=6?

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Answer 1 · 2018-01-11T19:16:24

#x = -13/2, y = -7# (one solution)

#8x-5y = -17#
#-2x+y= 6# (*4)

#8x-5y = -17#
#-8x+4y= 24#

add both together:

#0x -1y = 7#

#-y = 7#

multiply by #-1#:

#y = -7#

#-2x+y= 6#

substitute #y# for the value found:

#-2x-7 = 6#

add #7#:

#-2x = 13#

divide by #2#:

#x = -13/2#

on a graph, there is only one point of intersection,
at #(-6.5, 7):#
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