maths question - simultaneous equations

i solved the sim equation but idk how to do part 2.
q3

How many times would you expect a line to cut a curve?

0 - they do not interesect
2 - they cross twice
You've found there's just one solution so what does that tell you?

that the discriminant is equal to 0? idk

How many times would you expect a line to cut a curve?

0 - they do not interesect
2 - they cross twice
You've found there's just one solution so what does that tell you?

ohhhhhhhh now i get it. i need to find the discriminant of the new equation

No - just finding that you have one solution [effectively two equal roots] tells you immediately that its a tangent.

So you have found that there is only one place where the two lines meet (when x=4)

If there were two solutions, the lines would cross twice and if there were no solutions, the lines wouldn't cross at all and there would be no solutions.

Think about what a tangent actually is and you will see how by solving the equation and finding only one solution, y=2x-14 has to be a tangent

thank youuuuu