SOLUTION: need to solve the equation using the substitution method: 3x+4y=6, 2x+8y=9 5x+20y=3, 6x+7y=45

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Question 854967: need to solve the equation using the substitution method:
3x+4y=6, 2x+8y=9
5x+20y=3, 6x+7y=45
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Either there are typos, or whoever made up this problem meant to torture students with calculations.

Substitution is not the best method to solve systems like
system%283x%2B4y=6%2C+2x%2B8y=9%29 or system%285x%2B20y=3%2C+6x%2B7y=45%29 .
Substitution works best when one of the coefficients is 1 or -1 .
You look for a coefficient that is "friendly" and solve for that variable.
When none of the coefficients is 1 or -1 substitution makes you work with cumbersome fractions.

For system%283x%2B4y=6%2C+2x%2B8y=9%29 I would solve 2x%2B8y=9 for x ,
2x%2B8y=9 --> 2x=-8y%2B9 --> x=-8y%2F2%2B9%2F2 --> x=-4y%2B9%2F2 ,
and then I would substitute -4y%2B9%2F2 for x in the other equation:
system%283x%2B4y=6%2C+x=-4y%2B9%2F2%29 --> 3%2A%28-4y%2B9%2F2%29%2B4y=6-->-12y%2B27%2F2%2B4y=6-->-8y%2B27%2F2=6-->27%2F2-6=8y-->27%2F2-12%2F2=8y-->15%2F2=8y-->y=15%2F2%2F8-->highlight%28y=15%2F16%29 .
Then system%28y=15%2F16%2C+x=-4y%2B9%2F2%29 --> x=-4%2A%2815%2F16%29%2B9%2F2-->x=-15%2F4%2B9%2F2-->x=-15%2F4%2B18%2F4-->highlight%28x=3%2F4%29

For system%285x%2B20y=3%2C+6x%2B7y=45%29 I would solve 5x%2B20y=3 for x ,
5x%2B20y=3-->5x=-20y%2B3-->x=-20y%2F5%2B3%2F5-->x=-4y%2B3%2F5 ,
and then I would substitute -4y%2B3%2F5 for x in the other equation:
system%28x=-4y%2B3%2F5%2C+6x%2B7y=45%29 --> 6%2A%28-4y%2B3%2F5%29%2B7y=45-->-24y%2B18%2F5%2B7y=45-->-17y%2B18%2F5=45-->-17y=45-18%2F5-->-17y=225%2F5-18%2F5-->-17y=207%2F5-->y=207%2F5%2F%28-17%29-->highlight%28y=-207%2F85%29 .
Then system%28x=-4y%2B3%2F5%2C+y=-207%2F85%29 -->x=-4%2A%28-207%2F85%29%2B3%2F5-->x=828%2F85%2B51%2F85-->highlight%28x=879%2F85%29