Question

Make an equation with no solution

Answer 1

An equation with no solution:

2x+5=2x-3

Answer 2

Answer:

$f(x)=\frac{4}{3}x+1$

Step-by-step explanation:

The graphed function is:

$f(x)=\frac{4}{3} x-2$

Now, a system of linear equations with no solution means 2 lines that never intersect at any point. The only way that can be true is if both lines are parallel, or have the same slope.

You can write any equation that has the same slope, I'll do this one:

$f(x)=\frac{4}{3}x+1$

You can confirm that they are parallel in the attached image.

The reason they cannot intersect is because the point at which 2 lines intersect is the solution. If they intersect at any point, there is a solution, and that solution is that point.