SOLUTION: Solve the system of equations by substitution {{{system(2x+3y=13.50,3x+2y=16.50)}}}

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Question 284546: Solve the system of equations by substitution
system%282x%2B3y=13.50%2C3x%2B2y=16.50%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by substitution

system%282x%2B3y=13.50%2C3x%2B2y=16.50%29

Solve the first equation for x

2x%2B3y=13.50
2x=13.50-3y

 Divide every term by 2

x=6.75-1.5y

Substitute %286.75-1.5y%29 for x in the second equation:

3x%2B2y=16.50

3%286.75-1.5y%29%2B2y=16.50

Distribute the 3 into the parentheses:

20.25-4.5y%2B2y=16.50

Combine like terms:

20.25-2.5y=16.50

Add -20.25 to both sides:

-2.5y=-3.75

Divide both sides by -2.5

y=1.5

Substitute %281.5%29 for y in 

x=6.75-1.5y

x=6.75-1.5%281.5%29

x=4.5

Solution: (x,y) = (4.5,1.5)

Edwin