Create a system of linear equations that when solved algebraically, prove to have no solution.

Suppose we have the following system of equations:

2y + 6x = 20

y + 3x = 15

We solve the system:

y = - 3x + 15

Substituting in equation 1:

2 (-3x + 15) + 6x = 20

-6x + 30 + 6x = 20

0 = - 10

Therefore, the system has no solution.

Answer:

a system of linear equations that has no solutions is:

2y + 6x = 20

y + 3x = 15