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if a+b=1000, and 7a+15b=11504, what is value of a and b?

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First you have to solve for one of the variables in terms of the other.  Take one of the equations for example a+b=1000 and  solve for a to get a=1000-b.  Now you can substitute this expression into the other equation instead of a.  7a+15b=11504 becomes 7(1000-b)+15b=11504.   Now we expand the parenthesis 7000-7b+15b. Combine like terms 7000+8b=11504. Subtract 7000 from both sides 8b=4504.  Divide both sides by 8, b=563.  Now you can substitute b into either of the original expressions and solve for a.  It's best to use the easier one.  a+563=11504.  a=437.  Hope this helps.