https://file.aiquickdraw.com/mathbot/file/1738802311578xdj6rf3x.jpg

This image shows the graphical solution of a system of linear equations. Let's break it down:

1. The system of equations:
   - \( 2x + y = 5 \) (Equation 1)
   - \( x - 2y = 10 \) (Equation 2)

2. The steps for solving this system graphically:
   - First, the equations are rewritten in slope-intercept form (\( y = mx + b \)):
     - From the first equation \( 2x + y = 5 \), solving for \( y \), you get \( y = -2x + 5 \) (This is in the form \( y = mx + b \), where the slope \( m = -2 \) and the y-intercept \( b = 5 \)).
     - From the second equation \( x - 2y = 10 \), solving for \( y \), you get \( y = \frac{x - 10}{2} \), or equivalently, \( y = \frac{1}{2}x - 5 \) (This is also in the form \( y = mx + b \), where \( m = \frac{1}{2} \) and \( b = -5 \)).

3. The graph of both equations would be plotted, and the intersection point of the two lines gives the solution to the system of equations.

If you want a more detailed breakdown of these steps or additional calculations, feel free to ask!

Would you like further explanation on graphing systems of equations, or is there another area you'd like to explore?

Here are 5 related questions to deepen your understanding:
1. How do you solve systems of equations using substitution?
2. What is the significance of the slope and y-intercept in a linear equation?
3. How can you check the solution to a system of equations algebraically after solving graphically?
4. What would the solution look like if the system had parallel lines?
5. How does the method of graphing compare with solving systems algebraically (substitution/elimination)?

Tip: When graphing, always ensure that both equations are in slope-intercept form for easier identification of the slope and intercept.

Solve the system of equations graphically: 2x + y = 5 and x - 2y = 10.

Learn how to solve the system of equations 2x + y = 5 and x - 2y = 10 graphically. This step-by-step guide explains converting equations to slope-intercept form, graphing, and identifying intersection points. Suitable for Grades 8-10.

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