Question 199905
(1) -7x +y =4,,,,,,or y = 4+7x
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(2) 2x +8y =0
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subst  from (1)  into  (2),,  2x + 8(4+7x) =0
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2x +32+56x =0
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58x =-32
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x=-32/58 = - .552
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subst  in  (1),, y = 4 + 7(-.552) = .138
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check  by  subst  into  originals
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(1) -7(-.552) +(.138) =4,,,, 3.864 +.138 = 4,,,ok
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(2) 2(-.552) +8 (.138) = -1.104 +1.104 =0,,,,,ok
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info,  if  there  were  " no  solutions"  it  would  mean  that  the  lines  were " parallel",  and  never  intersect.  If  you  didn"t  recognize  this  from  equal  slopes,  doing  the  math  would  result  in  a  statement  that  is  "always  not  true" ,  such  as  6=7
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if  there  were  infinite  solutions,  the  lines  would  be " coincident" , or  lay  on  top  of  each  other.  If this  was  not  recognized  the math  would  result  in a  statement  that  is  " always  true", such  as  6=6.