How many solutions does the system have?

12 X -15 Y equals 18
4X minus 5Y equals six

1 answer

This system of equations can be simplified to:

1) 12X - 15Y = 18
2) 4X - 5Y = 6

To find how many solutions the system has, we can rearrange the second equation to solve for X in terms of Y:

4X = 6 + 5Y
X = (6 + 5Y) / 4

Then, substitute this expression for X into the first equation:

12((6 + 5Y) / 4) - 15Y = 18
(18 + 15Y) - 15Y = 18
18 = 18

Since the equation simplifies to 18=18, this means that there are infinitely many solutions to this system of equations.