Question 54259: 3/7x + 5/9y = 27
1/9x + 2/7y = 7
Solve each system by the addition method
can someone who understands this help thank you
Answer by jenrobrody(19)   (Show Source):
You can put this solution on YOUR website! 3/7x + 5/9y = 27
1/9x + 2/7y = 7
It may be easier to cancel out fractions by multiplying both sides by LCD=63
63(3/7x + 5/9y) = 63(27) AND 63(1/9x +2/7y) = 63(7)
189/7x + 315/9y = 1701; ; 63/9x + 126/7y = 441
27x + 35y = 1701; ; 7x + 18y = 441
so we have an equivalent problem: 27x + 35y = 1701
7x + 18y = 441
to cancel out x's, we need 189x and -189x
multiply first equation by 7: 189x + 245y = 11907
multiply second equation by -27: -189x - 486y = -11907
add: 0x -241y = 0
-241y = 0
y = 0
substitute into either equation to solve for x:
3/7x + 5/9(0) = 27
3/7x = 27
(7/3)(3/7x) = (7/3)(27)
x = 63
(x,y)=(63,0)
check:
3/7(63) + 5/9(0) = 9*7 + 0 = 27
1/9(63) + 2/7(0) = 63/9 + 0 = 7
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