Create a system of linear equations that when solved algebraically, prove to have no solution.
One possible system of linear equations that has no solution is:
x + y = 5
2x + 2y = 9
If we try to solve this system algebraically, we can use the first equation to express y in terms of x:
y = 5 - x
Substituting this expression for y into the second equation, we get:
2x + 2(5 - x) = 9
Simplifying this equation, we get:
2x + 10 - 2x = 9
This simplifies further to:
10 = 9
Since this is a contradiction (10 cannot be equal to 9), there is no solution to this system of linear equations.