Question

# What should be subtracted from $$2a+8b+10$$ to get $$-3a+7b+16$$

Solution

## Let the value to be subtracted from $$2a + 8b + 10$$ to get $$-3a+7b+16$$ be $$xa +yb+z$$.Therefore,$$(2a+8b+10)-(xa+yb+z)=-3a+7b+16$$$$\implies (2-x)a+(8-y)b+10-z=-3a+7b+16$$On comparing coefficients,$$2-x=-3 \implies x=5$$$$8-y=7 \implies y=1$$$$10-z=16 \implies z=-6$$Hence, the required value is $$5a +b-6$$.Maths

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