Question 364352
One's a ellipse, one's a line.
1. {{{2y^2+x^2=4}}}
2.{{{y+x=3}}}
From eq. 2,
{{{y=3-x}}}
Substitute into eq. 1,
{{{2(3-x)^2+x^2=4}}}
{{{2(9-6x+x^2)+x^2=4}}}
{{{18-12x+2x^2+x^2=4}}}
{{{3x^2-12x+18=4}}}
{{{3x^2-12x+14=0}}}
There are no real solutions which means the line and the ellipse do not intersect.
.
.
.
{{{drawing(300,300,-4,4,-4,4,grid(1),
graph(300,300,-4,4,-4,4,0,sqrt((4-x^2)/2)),
graph(300,300,-4,4,-4,4,0,-sqrt((4-x^2)/2),3-x)
)}}}