y = 2x + 1 and y = x + 3: (2, 5)
y = x + 3 and y = -3x - 2: (-5/4, 1/4)
y = x + 3 and y = -x - 7: (-5, -2)
y = -x - 7 and y = -x - 7: Any point on the line, (-1, -8) for example.
y = x + 3 and y = 2x + 1: (-2, 1)
y = 2x + 1 and y = -3x - 2: (-3/5, -1/5) .
The point of intersection occurs when two equations are equal at the same x and y values.
Let's analyze each system:
y = 2x + 1 and y = x + 3:
Setting both equations equal: 2x + 1 = x + 3 -> x = 2 -> y = 2(2) + 1 = 5.
Point of intersection: (2, 5).
y = x + 3 and y = -3x - 2:
Setting both equations equal: x + 3 = -3x - 2 -> 4x = -5 -> x = -5/4 -> y = -5/4 + 3 = 1/4.
Point of intersection: (-5/4, 1/4).
y = x + 3 and y = -x - 7:
Setting both equations equal: x + 3 = -x - 7 -> 2x = -10 -> x = -5 -> y = -5 + 3 = -2.
Point of intersection: (-5, -2).
y = -x - 7 and y = -x - 7:
Identical equations, meaning they overlap completely. Any point on this line will be the intersection point.
We can choose (-1, -8) for example.
y = x + 3 and y = 2x + 1:
Setting both equations equal: x + 3 = 2x + 1 -> x = -2 -> y = -2 + 3 = 1.
Point of intersection: (-2, 1).
y = 2x + 1 and y = -3x - 2:
Setting both equations equal: 2x + 1 = -3x - 2 -> 5x = -3 -> x = -3/5 -> y = 2(-3/5) + 1 = -1/5.
Point of intersection: (-3/5, -1/5).