SOLUTION: Hi Find positive intergers x and y that satisfy the rule 9x + 6y = 90 Thanks

Question 1183263: Hi
Find positive intergers x and y that satisfy the rule 9x + 6y = 90
Thanks

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
9x + 6y = 90
solve for y to get:
y = 15 - 1.5x

since y = 1.5 * x, and since y has to be an integer, then:
x has to be an even number from 2 to 8.

when that happens, y will be equal to 15 - 1.5 * x.

your solutions are shown in the following graph.

the coordinate points are in (x,y) format.

for example, (2,12) means the value of y is 12 when the value of x is 2.

the eqution is 9x + 6y = 90
then y = 12 and x = 2, the equation becomes:
9*2 + 6*9 = 90 which becomes:
18 + 72 = 90 which becomes:
90 = 90, confirmirming those value pairs are correct.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

x and y are positive integers, so 2y is an even number; and 30 is an even number.

That means 3x must be an even number; and that means x is a (positive) even integer.

Find the solutions by enumeration.

x=2: 6+2y=30; 2y=24; y=12 (x,y)=(2,12)
x=4: 12+2y=30; 2y=18; y=9 (x,y)=(4,9)
x=6: 18+2y=30; 2y=12; y=6 (x,y)=(6,6)
x=8: 24+2y=30; 2y=6; y=3 (x,y)=(8,3)

Higher values of x will yield zero or negative values of y, so that list of 4 solutions is the complete list.

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