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Using a sheet of graph paper, solve the following system of equations graphically.

Be sure to show your work, use a straight edge, and be neat. When you are finished, enter the solution set in the box below. Turn in your graph paper to your teacher or upload an image or a screenshot of your graph.

[tex]\[
\begin{array}{l}
x + y = 0 \\
x - y + 2 = 0
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the given system of equations graphically step by step.

We have the following system of equations:

[tex]\[ \begin{array}{l} x + y = 0 \\ x - y + 2 = 0 \end{array} \][/tex]

### Step 1: Rearrange the Equations
First, let's rearrange the equations to express [tex]\( y \)[/tex] explicitly in terms of [tex]\( x \)[/tex] so we can graph them easily.
1. For the first equation [tex]\( x + y = 0 \)[/tex], we get:
[tex]\[ y = -x \][/tex]

2. For the second equation [tex]\( x - y + 2 = 0 \)[/tex], we get:
[tex]\[ x - y = -2 \implies -y = -x - 2 \implies y = x + 2 \][/tex]

So, our system now looks like:
[tex]\[ \begin{array}{l} y = -x \\ y = x + 2 \end{array} \][/tex]

### Step 2: Plot the Equations
Next, we can plot these two equations on graph paper.

Equation 1: [tex]\( y = -x \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]. So, one point is (0, 0).
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex]. So, another point is (1, -1).
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]. Another point is (-1, 1).

Equation 2: [tex]\( y = x + 2 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex]. So, one point is (0, 2).
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 3 \)[/tex]. Another point is (1, 3).
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]. Another point is (-1, 1).

### Step 3: Draw the Lines
Using a straight edge, carefully draw the two lines based on the points:

- For [tex]\( y = -x \)[/tex]:
- Connect the points (0, 0), (1, -1), and (-1, 1).

- For [tex]\( y = x + 2 \)[/tex]:
- Connect the points (0, 2), (1, 3), and (-1, 1).

### Step 4: Find the Intersection
The solution to the system of equations is where the two lines intersect.

By looking at the points we noted:
- For [tex]\( y = -x \)[/tex]: the point (-1, 1)
- For [tex]\( y = x + 2 \)[/tex]: the point (-1, 1)

We can see that both lines intersect at the point [tex]\((-1, 1)\)[/tex].

### Solution Set
The solution to the system of equations is:
[tex]\[ (x, y) = (-1, 1) \][/tex]

So, your final solution set is [tex]\((-1, 1)\)[/tex].

Please make sure to neatly draw the graphs on graph paper, label each equation, and highlight the intersection point for clarity. Then submit your graph paper as instructed.
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