Without solving the following linear system, determine whether there are no solutions, one solution, or infinite solutions

2*x* + 3*y* = 1

4*x* + 6*y* = 4

We can first rewrite these equations in slope-intercept form

2*x* + 3*y* = 1 → *y* = *x *+

4*x* + 6*y* = 4 → *y* = *x *+

Because these two lines have the same slope but different *y*-intercepts, they will never intersect and there are no solutions to this linear system.