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Answer:
[tex]a = -5 ~, b = -1[/tex]
Step-by-step explanation:
The first term in the pair is equal to the first term in the second pair. Using this, we can set an equality statement for the pairs and then use algebra to solve for each term.
Solving:
[tex]\section*{}Given the equation:\[(2a, 2b+3) = (-10, -b)\]Split this into two separate equations:\[\begin{cases}2a = -10 \\2b + 3 = -b\end{cases}\]\\\hrulefill[/tex]
[tex]\hrulefill[/tex]
[tex]\subsection*{Solving for \(a\):}\[2a = -10\]Divide both sides by 2:\[\boxed{a = -5}\]\hrulefill\subsection*{Solving for \(b\)}\[2b + 3 = -b\]Add \(b\) to both sides:\[2b + b + 3 = 0\]\[3b + 3 = 0\]Subtract 3 from both sides:\[3b = -3\]Divide both sides by 3:\boxed{b = -1}\]\hrulefill[/tex]
Therefore, a = -5 and b = -1.