anonymous
  • anonymous
x + y = 6 2x - y = 3 The system of equations? a. has no solution b. has one solution c. is coincident
Algebra
katieb
  • katieb
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DanJS
  • DanJS
a quick check if the two equations are the same line (coincident), if one is a multiple of the other, they are the same lines..
DanJS
  • DanJS
look, what do you multiply x by to get the 2x in the second.... 2 is y in the second also 2 times the first...here it is not
DanJS
  • DanJS
so not c

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DanJS
  • DanJS
no solutions mean they are parallel, same slopes, if you want to put them both in y=mx+ b and see if they have same m
wolf1728
  • wolf1728
Solve for x and y Add both equations: A) x + y = 6 B) 2x - y = 3 3x =9 Therefore x =3 Substitute x=3 into A) x + y = 6 to get the y value
anonymous
  • anonymous
\[x+y=6\\2x-y=3\\ ratios\ of\ their\ coefficients\ are\ \not\ equal\\i.e.\ \frac{ 1 }{ 2 }\neq \frac{ 1 }{ -1 }\\so\ system\ has\ unique\ solution\\ clearly\ \it\ has\ one\ solution\ (option,b)\]
anonymous
  • anonymous
please replace 'are equal' by 'are not equal'

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