To find the intersection, set the two expressions for y equal:
-x + 7 = 3x + 3
Bring x terms to one side and constants to the other:
7 - 3 = 3x + x
4 = 4x ⇒ x = 1
Now substitute x = 1 into either equation to get y:
y = 3(1) + 3 = 6
So the solution (the intersection point) is (1, 6).
Graphing check:
- For y = -x + 7: y-intercept (0,7). Slope -1 gives another point (1,6).
- For y = 3x + 3: y-intercept (0,3). Slope 3 gives the point (1,6) as well.
Both lines pass through (1, 6), so the solution is (1, 6).