The system of equations for the given lines is confirmed by substituting coordinates where they intersect the axes. Verifying with points like (-3, 9) ensures consistency in both red (y = -2x + 3) and green (y = 1/2x - 1) lines.
The system of equations for the graphed lines below is:
- Red line: y = -2x + 3
- Green line: y = 1/2x - 1
You can verify this by substituting the coordinates of the points where the lines intersect the axes or each other into the equations and checking if they are true. For example, the red line passes through the point (-3, 9), so if we plug in x = -3 and y = 9 into the equation y = -2x + 3, we get:
9 = -2(-3) + 3
9 = 6 + 3
9 = 9
This is true, so the point (-3, 9) lies on the red line. You can do the same for the other points and lines.