Question

solve this system of equations by using graphing.

\\\

$$\begin{cases} y = \\frac{1}{2}x + 1 \\\\ y = -\\frac{1}{2}x - 3 \\end{cases}$$

\\

\\((?, \quad)\\)

Explanation:

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<reasoning>

Identify the system of equations

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = \frac{1}{2}x + 1 \\ &y = -\frac{1}{2}x - 3 \end{aligned}$$

\]

Locate the intersection point on the graph

Using the Coordinate Plane and Ordered Pairs knowledge points
\[

$$\begin{aligned} &\text{Intersection point: } (x, y) = (-4, -1) \end{aligned}$$

\]

Verify the intersection algebraically

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{For } y = \frac{1}{2}x + 1: \quad -1 = \frac{1}{2}(-4) + 1 = -2 + 1 = -1 \quad (\text{True}) \\ &\text{For } y = -\frac{1}{2}x - 3: \quad -1 = -\frac{1}{2}(-4) - 3 = 2 - 3 = -1 \quad (\text{True}) \end{aligned}$$

\]
</reasoning>

<answer>
Solve this system of equations by using graphing.
\[

$$\begin{cases} y = \frac{1}{2}x + 1 \\ y = -\frac{1}{2}x - 3 \end{cases}$$

\]
The solution is (<blank>-4</blank>, <blank>-1</blank>).
</answer>

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Answer:

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<reasoning>

Identify the system of equations

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = \frac{1}{2}x + 1 \\ &y = -\frac{1}{2}x - 3 \end{aligned}$$

\]

Locate the intersection point on the graph

Using the Coordinate Plane and Ordered Pairs knowledge points
\[

$$\begin{aligned} &\text{Intersection point: } (x, y) = (-4, -1) \end{aligned}$$

\]

Verify the intersection algebraically

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{For } y = \frac{1}{2}x + 1: \quad -1 = \frac{1}{2}(-4) + 1 = -2 + 1 = -1 \quad (\text{True}) \\ &\text{For } y = -\frac{1}{2}x - 3: \quad -1 = -\frac{1}{2}(-4) - 3 = 2 - 3 = -1 \quad (\text{True}) \end{aligned}$$

\]
</reasoning>

<answer>
Solve this system of equations by using graphing.
\[

$$\begin{cases} y = \frac{1}{2}x + 1 \\ y = -\frac{1}{2}x - 3 \end{cases}$$

\]
The solution is (<blank>-4</blank>, <blank>-1</blank>).
</answer>

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