https://file.aiquickdraw.com/mathbot/file/1726198283208hiu2qmj2.jpg

To solve the system of equations by graphing, we need to plot both equations on the same coordinate plane and find their point of intersection.

The system of equations is:
1. \(x + y = 2\)
2. \(x - 2y = 8\)

### Step 1: Rewrite Each Equation in Slope-Intercept Form

**Equation 1:**
\[
x + y = 2
\]
Solve for \(y\):
\[
y = -x + 2
\]

**Equation 2:**
\[
x - 2y = 8
\]
Solve for \(y\):
\[
-2y = -x + 8 \implies y = \frac{1}{2}x - 4
\]

### Step 2: Graph Both Equations

1. **Graph the first equation** \(y = -x + 2\):
   - The y-intercept is 2 (point: \((0, 2)\)).
   - The slope is -1, so from the y-intercept, move down 1 unit and right 1 unit to plot the next point (point: \((1, 1)\)).

2. **Graph the second equation** \(y = \frac{1}{2}x - 4\):
   - The y-intercept is -4 (point: \((0, -4)\)).
   - The slope is \(\frac{1}{2}\), so from the y-intercept, move up 1 unit and right 2 units to plot the next point (point: \((2, -3)\)).

### Step 3: Find the Point of Intersection

Now we need to find the point where these two lines intersect. Let's solve the system algebraically to find the intersection point:

Set the equations equal to each other:
\[
-x + 2 = \frac{1}{2}x - 4
\]

Combine like terms:
\[
-2x + 4 = x - 8
\]

Simplify and solve for \(x\):
\[
-2x - x = -8 - 4 \implies -3x = -12 \implies x = 4
\]

Substitute \(x = 4\) back into one of the equations (e.g., \(y = -x + 2\)):
\[
y = -4 + 2 = -2
\]

### Solution:
The point of intersection is \((4, -2)\). 

Therefore, the solution to the system of equations is:
\[
\boxed{(4, -2)}
\]

Would you like me to provide a graph to visualize this solution? Also, feel free to ask any of the following questions:

1. How do you graph linear equations with different slopes?
2. Can you explain more about the slope-intercept form of a line?
3. How do you determine the solution of a system of equations by graphing?
4. What happens if two lines are parallel when solving by graphing?
5. How can I check if my solution is correct after solving graphically?

**Tip:** Always double-check your plotted points to ensure accuracy when solving systems by graphing!

Solve the following system of equations by graphing: x + y = 2 and x - 2y = 8.

Learn how to solve the system of linear equations x + y = 2 and x - 2y = 8 by graphing. This problem involves graphing lines, finding their intersection point, and applying the slope-intercept form. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation