Do these points intersect? 5x + 6y = -5.5 & 6x + 1.5y = -8.5. My answer is yes and point of intersection is -1.5, 0.33. Is it correct?

Slope of the first line = -5/6
Slope of the second line = -6/1.5 = -4
The slopes of the two lines are not equal. Hence, they are not parallel.

The two line intersect at a point because they are not parallel.


5x + 6y = -5.5 …… [1]
6x + 1.5y = -8.5 …… [2]

[2] × 4 :
24x + 6y = -34 …… [3]

[3] - [1] :
(24x - 5x) + (6y - 6y) = (-34) - (-5.5)
19x = -28.5
x = -3/2

Put x = -1.5 into [2] :
6(-1.5) + 1.5y = -8.5
-9 + 1.5y = -8.5
1.5y = 0.5
y = 1/3

The two lines intersect at (x, y) = (-3/2, 1/3)

Do these points intersect? 5x:6y is not proportional to 6x:1.5y, so yes, they do intersect. {No calculation to this point, just observation.}

If you need it, the point of intersection is ((-5.5×1.5-6×-8.5)/(5×1.5-6×6), (5×-8.5--5.5×6)/(5×1.5-6×6)) which simplifies to (-³∕₂, ⅓).

5x + 6y = -5.5
6x + 1.5y = -8.5
These lines intersect.
Point of intersection:
x ≈ -1.5, y ≈ 0.333333