Tell whether the system has one solution, infinitely many solutions or no solutions. 2x-5y=17 and 6x-15y=51
The equations are,
2x – 5y = 17
6x – 15y = 51
Putting them into standard form,
y = (2/5)x – 17/5
y = (6/15)x – 51/15 = (2/5)x – 17/5
The two equations are equations of straight lines with the same slope (m = 2/5) and with the same y-intercept (c = -17/5).
This means that the two lines are co-linear. They lie on top of each other, so there are an infinite number of points of intersection.
Answer: There are infinitely many solutions.