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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 $$5a +b-6$$.

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