Question

verify whether the given point is a solution for the system of linear equations.
a. \\(y = 4x + 9\\) and \\(y = -3x - 5\\); \\((-2, 1)\\)

Explanation:

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<reasoning>

Substitute the point into the first equation

\[

$$\begin{aligned} &\text{Point: } (-2, 1) \implies x = -2, \quad y = 1\\ &\text{Equation 1: } y = 4x + 9\\ &1 = 4(-2) + 9\\ &1 = -8 + 9\\ &1 = 1 \quad (\text{True}) \end{aligned}$$

\]

Substitute the point into the second equation

\[

$$\begin{aligned} &\text{Equation 2: } y = -3x - 5\\ &1 = -3(-2) - 5\\ &1 = 6 - 5\\ &1 = 1 \quad (\text{True}) \end{aligned}$$

\]

Determine the final verification result

\[
\text{Since } (-2, 1) \text{ satisfies both equations, it is a solution.}
\]
</reasoning>

<answer>
Yes, the point \((-2, 1)\) is a solution for the given system of linear equations.
</answer>

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Answer:

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<reasoning>

Substitute the point into the first equation

\[

$$\begin{aligned} &\text{Point: } (-2, 1) \implies x = -2, \quad y = 1\\ &\text{Equation 1: } y = 4x + 9\\ &1 = 4(-2) + 9\\ &1 = -8 + 9\\ &1 = 1 \quad (\text{True}) \end{aligned}$$

\]

Substitute the point into the second equation

\[

$$\begin{aligned} &\text{Equation 2: } y = -3x - 5\\ &1 = -3(-2) - 5\\ &1 = 6 - 5\\ &1 = 1 \quad (\text{True}) \end{aligned}$$

\]

Determine the final verification result

\[
\text{Since } (-2, 1) \text{ satisfies both equations, it is a solution.}
\]
</reasoning>

<answer>
Yes, the point \((-2, 1)\) is a solution for the given system of linear equations.
</answer>

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