Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
x, plus, 5, y, equals, 2
x+5y=
2
3, x, plus, 15, y, equals, 8
3x+15y=
8

Answer 1

This system of equations has no solutions. If we try to solve it, we get:

From the first equation:
x + 5y = 2
x = 2 - 5y

Substitute x = 2 - 5y into the second equation:
3(2-5y) + 15y = 8
6 - 15y + 15y = 8
6 = 8

Since the result is not a true statement (6 does not equal 8), the system of equations has no solutions.