Question

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

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.