Hi. This are non-linear equations and I don't know whether to equate them together to get the graph or something.
Y^2-2x+2=0 and x-y-5=0
2x^2+3y^2=21 and 3x^2-4y^2=23
to get the graph, just graph them...
To find where the graphs intersect, solve algebraically
y^2-2x+2=0 and x-y-5=0
x=y+5, so
y^2-2(y+5)+2 = 0
y^2-2y-8 = 0
(y-4)(y+2) = 0
Now you know y, so you can get the corresponding x values.
2x^2+3y^2=21
3x^2-4y^2=23
8x^2+12y^2 = 84
9x^2-12y^2 = 69
17x^2 = 153
x^2 = 9
Now you have x, and you can get the y values