y=5x+7
3y−15x=18
x−2y=6
3x−6y=18
y = 3x + 6
y=−13x−4
y=23x−1
y=23x−2
infinite solutions
no solutions
One Solutions
- Infinite solutions: y=3x+6, y=23x-1, and y=23x-2 are parallel lines that never intersect, so there are no distinct solutions and infinitely many overlapping solutions.
- No solutions: these types of systems have lines that are parallel and never intersect, leading to no solutions. This is the case for y=-13x-4 and x-2y=6.
- One solution: this means that there is only one point where both lines intersect, giving a single solution. This is the case for y=5x+7 and 3y-15x=18 as they both intersect at the point (3,22). Similarly, x-2y=6 and 3x-6y=18 intersect at the point (6,-3).