SOLUTION: 36x+54y=450 12x+15y=135

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Question 1205740: 36x+54y=450 12x+15y=135
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

36x%2B54y=450 ......eq.1
12x%2B15y=135.....eq.2....both sides multiply by+3
---------------------
36x%2B54y=450 ......eq.1
36x%2B45y=405.....eq.2
---------------------------subtract eq.2 from eq.1
36x%2B54y-%2836x%2B45y%29=450-405
36x%2B54y-36x-45y=45
9y=45
y=45%2F9
y=5
go to eq.1, substitute+y
36x%2B54%2A5=450
36x%2B270=450
36x=450-270
36x=180
x=180%2F36
x=5
solution:
ordered pair (5,5)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
36x + 54y = 450
12x + 15y = 135

leave first equation as is and multiply second equation by 3 to get:
36x + 54y = 450
36x + 45y = 405

subtract second equation from first to get:
9y = 45

solve for y to get:
y = 5

replace y with 5 in first equation and solve for x to get:
36x + 54y = 450 becomes 36x + 54 * 5 = 450 which becomes 36x + 270 = 450.

subtract 270 from both sides of the equation to get:
36x = 450 - 270

simplify to get:
36x = 180

solve for x to get:
x = 180/36 = 5

replace x with 5 and y with 5 in the second original equation to get:
12x + 15y = 135 becomes 12 * 5 + 15 * 5 = 135 which becopmes:
60 + 75 = 135 which becomes 135 = 135.

this confirms the values of x = 5 and y = 5 satisfies both original equations.
that's your solution.