SOLUTION: Need help on the following problem please? problem: determine which variable you will substitute for and rewrite as an equation using one variable? x + y =6 2x

SOLUTION: Need help on the following problem please? problem: determine which variable you will substitute for and rewrite as an equation using one variable? x + y =6 2x - 3y =9

Question 159312: Need help on the following problem please?
problem:
determine which variable you will substitute for and rewrite as an equation using one variable?
x + y =6
2x - 3y =9
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
equations are:
x + y =6
2x - 3y =9
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in the first equation you can solve for x or y in terms of the other.
it's easier to do this then solving for x or y in the second equation because the calculations look simpler. i solved for x in terms of y.
x + y = 6 becomes x = 6 - y so (6-y) is placed in the second equation everywhere that x appears.
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the second equation of 2*x - 3*y becomes 2*(6-y) -3*y = 9 which becomes 12 - 2*y - 3*y = 9 which becomes 12 - 5*y = 9 which becomes 12 - 9 = 5*y which becomes 3 = 5*y which becomes y = 3/5.
going back to the first equation x + y = 6, substitute 3/5 for y and the equation becomes x + 3/5 = 6 which becomes x = 6-(3/5) which becomes x = 30/5 - 3/5 which becomes x = 27/5.
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in the first equation 27/5 + 3/5 = 30/5 = 6 so the first equation checks out ok.
in the second equation 2*(27/5) - 3*(3/5) = 9 which becomes 54/5 - 9/5 = 9 which becomes 45/5 = 9 which becomes 9 = 9 so the second equation checks out ok as well.

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