Question

Which line will have no solution with the parabola y – x + 2 = x2?

y = –3x –3
y = –2x –3
y = 2x –3
y = 3x –3

Answer 1

The line y = 2x - 3 will have no solution with the given parabora. All other lines gives a real solution except the line y = 2x - 3

Answer 2

You can solve this question graphically.

First, plot all graphs of given functions:

• 
  `y - x + 2 = x^2 \Rightarrow y=x^2+x-2` - red curve;
• 
  `y = -3x -3` - blue line;
• 
  `y = -2x -3` - green line;
• 
  `y = 2x -3` - orange line;
• 
  `y = 3x -3` - violet line.

Then see whether parabola and line have common points. Only orange line doesn't intersect red curve, this means that system

`\left\{\begin {array} {l}y=x^2+x-2 \\y=2x-3\end{array}\right.`

have no solution.

Answer: correct choice is C.