You have provided an image of a system of equations to be solved graphically. The system is:

$y = x - 1$ $x + 2y = 4$

To solve this graphically, we will plot each equation on the provided coordinate plane and find their point of intersection, which gives the solution.

Step 1: Plot the first equation $y = x - 1$

• This is already in slope-intercept form $y = mx + b$, where the slope $m = 1$ and the y-intercept is $b = -1$.
• Start by plotting the point (0, -1).
• Since the slope is 1, from the y-intercept, go up 1 unit and right 1 unit to get the next point (1, 0).
• Connect these points to draw the line.

Step 2: Rearrange and plot the second equation $x + 2y = 4$

• Solve for $y$: $2y = 4 - x \implies y = \frac{4 - x}{2} = -\frac{1}{2}x + 2$ This is also in slope-intercept form $y = -\frac{1}{2}x + 2$, where the slope is $-\frac{1}{2}$ and the y-intercept is 2.
• Start by plotting the point (0, 2).
• From this point, go down 1 unit and right 2 units (because the slope is $-\frac{1}{2}$) to plot another point (2, 1).
• Connect these points to draw the line.

Step 3: Find the point of intersection

• The lines will intersect at the solution to the system. By calculating or graphing, the intersection point is (2, 1).

So, the solution to the system is $(2, 1)$.

Would you like further details, such as how to verify this solution algebraically?

Here are 5 related questions to expand your understanding:

1. How do you verify a solution to a system of equations algebraically?
2. How would the graph change if the slope of the first equation was steeper (e.g., $y = 2x - 1$)?
3. What are other methods of solving systems of equations besides graphing?
4. Can systems of equations have no solution or infinitely many solutions?
5. How would this system change if you substituted the second equation with $x + 2y = 6$?

Tip: Always ensure both equations are in slope-intercept form when graphing, as this simplifies plotting the lines.