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Multiply by 2: $ 2a + 2b + 2c = 6 $
Subtract from (3):
Multiply (2) by 3: $ 3a + 3b + 3c = 9 $
Subtract from (4):
Now from (5): $ b = 2 - 3a $
Substitute into (6):
12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4 \Rightarrow a = \frac{4}{3}
Then $ b = 2 - 3 \cdot \frac{4}{3} = 2 - 4 = -2 $
From (2): $ \frac{4}{3} - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac{4}{3} = 5 - \frac{4}{3} = \frac{11}{3} $
And $ d = 2 $