How to solve systems of equations by graphing, including equations in slope-intercept form.

The image shows a system of two linear equations:

1. y = 2x - 3
2. y = -3x + 2

We are solving this system by graphing — meaning we want to find the point where the two lines cross (the solution).

Step 1: Understand slope-intercept form
Both equations are in the form y = mx + b, where:
- m is the slope (how steep the line is)
- b is the y-intercept (where the line crosses the y-axis)

For equation 1: y = 2x - 3
→ Slope (m) = 2
→ Y-intercept (b) = -3 → Start at (0, -3)

For equation 2: y = -3x + 2
→ Slope (m) = -3
→ Y-intercept (b) = 2 → Start at (0, 2)

Step 2: Graph both lines (mentally or on paper)
- For y = 2x - 3: From (0, -3), go up 2 units and right 1 unit to plot next point. Repeat.
- For y = -3x + 2: From (0, 2), go down 3 units and right 1 unit to plot next point. Repeat.

Step 3: Find where they intersect
Looking at the graph (or solving algebraically to verify), the lines cross at the point (1, -1).

Let’s check if (1, -1) satisfies both equations:

Equation 1: y = 2x - 3
Plug in x = 1 → y = 2(1) - 3 = 2 - 3 = -1 ✔

Equation 2: y = -3x + 2
Plug in x = 1 → y = -3(1) + 2 = -3 + 2 = -1 ✔

Both equations give y = -1 when x = 1 → So (1, -1) is correct.

Final Answer:
(1, -1)