Question

Write a system of linear equations that does not have a solution. Write each equation in y = mx + b form and explain why it does not have a solution.

Answer 1

For a system of linear equations to have no solution, they must be parallel. If you imagine the graph of two parallel lines, they can never intersect, meaning there cannot be a solution/a point that is on both lines.

For two lines to be parallel they must have the same slope, so the m value of both equations are the same. The b value can be any value you want, as long as they don't have the same b value (or else they'd be the same line! and the same lines have an infinite number of solutions).

One pair could be:
y=3x+3 and y=3x+9

But you can come up one yourself you'd like :)