ANSWER
[tex]x=-0.62[/tex] or [tex]x=1.62[/tex]
EXPLANATION
For [tex]-x^2+y=1[/tex]
We make y the subject to obtain,
[tex]y=x^2+1[/tex]
We can easily graph this function, because we just have to transform the graph of [tex]y=x^2[/tex] by shifting the intercept up to [tex]1[/tex].
As for the straight line, [tex]-x+y=2[/tex],
We find the intercepts as follows,
When [tex]y=0,x=-2[/tex].
When [tex]x=0,y=2[/tex].
We plot the points [tex](-2,0)[/tex] and
[tex](0,2)[/tex].
We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be
[tex]x=-0.62[/tex] or [tex]x=1.62[/tex]
See graph
