The answer is x = 34/19, y = 27/19
3y + 6x = 15
9y - x = 11
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Multiply the second eqution by 6:
3y + 6x = 15
54y - 6x = 66
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Sum up two equations:
3y + 54y = 15 + 66
57y = 81
y = 81/57
y = (81 : 3)/(57 : 3)
y = 27/19
Use the second equation to calculate x:
9y - x = 11
x = 9y - 11
x = 9 * 27/19 - 11
x = 243/19 - 11 * 19/19
x = 243/19 - 209/19
x = (243 - 209)/19
x = 34/19