Question

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

Answer 1

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.