Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Using a sheet of graph paper, solve the following system of equations graphically. Be sure to show any work, use a straight edge, and be neat. Include the solution set in your work.

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

Sagot :

GinnyAnswer
Sure, let's solve the system of equations graphically. The system of equations given is:

1. [tex]\( x + y = 0 \)[/tex]
2. [tex]\( x - y + 2 = 0 \)[/tex]

### Step 1: Graph the equations

#### For the first equation [tex]\( x + y = 0 \)[/tex]:

1. Rearrange to the slope-intercept form [tex]\( y = -x \)[/tex].
2. Determine two points that lie on this line:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex], so we have the point [tex]\( (0, 0) \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex], so we have the point [tex]\( (1, -1) \)[/tex].
3. Plot these points on the graph and draw a straight line through them.

#### For the second equation [tex]\( x - y + 2 = 0 \)[/tex]:

1. Rearrange to the slope-intercept form [tex]\( y = x + 2 \)[/tex].
2. Determine two points that lie on this line:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex], so we have the point [tex]\( (0, 2) \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 3 \)[/tex], so we have the point [tex]\( (1, 3) \)[/tex].
3. Plot these points on the graph and draw a straight line through them.

### Step 2: Identify the intersection point

1. Looking at the graph, find the point where the two lines intersect.
2. The point of intersection represents the solution to the system of equations.

### Step 3: Verify the solution set

By observing the graphs of both equations, the point where the lines intersect is [tex]\( (-1, 1) \)[/tex].

### Solution Set

The solution to the system of equations is [tex]\( x = -1 \)[/tex] and [tex]\( y = 1 \)[/tex]. Therefore, the solution set is:

[tex]\[ \{ (-1, 1) \} \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.