x = 2, y = 1
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1. 6x - 5y = 22 2. 5x - 9y = -1 1 times 5: 30x - 25y = 110 2 times 6: 30x - 54y = -6 Subtract : 29y = 116, so y = 4 and x therefore = 7
5x + 9y = 06x + 6y = 2 use substitution method5x + 9y = 0y = -5x/96x + 6y = 2 substitute y with -5x/96x + 6(-5x/9) = 26x - 30x/9 = 2 multiply by 9 to both sides54x - 30x = 1824x = 18x = 24/18 = 4/3y = -5x/9 = (-5/9)x substitute x with 4/3y = (-5/9)(4/3) = -20/27Thus the solution is x = 4/3 and y = -20/27.
-5x + y = -12- 3x + 6y = -12Since both of expressions have a value of -12, their sum is - 24. This is true only whenx = 20/9 and y = -8/9.-5x + y = -12y = 5x - 12- 3x + 6y = -12-3x + 6(5x - 12) = -12-3x + 30x - 72 = -1227x = 60x = 60/27x = 20/9y = 5x - 12y = 5(20/9) - 12y = 100/9 - 12y = (100 - 108)/9y = -8/9
(x+5)(x+5)
Oh, what a happy little math problem we have here! To factor 35x + 63y, we can first look for the greatest common factor of the coefficients, which is 7. Then we can factor out the 7 to get 7(5x + 9y). And just like that, we've created a beautiful and simplified expression!