$$ x+y=3 $$
$$ 2x^2 + y^2 = 5 $$
I solved it by substituting
$x = 3- y $
$2(3-y)^2 + y^2 =5 $
therefore, $ y= 2+\frac{i}{\sqrt3} $, $y= 2-\frac{i}{\sqrt3}$
However, I want to know that can I solve it by using the matrix inversion ?
2026-04-07 11:32:28.1775561548
Can the system $x+y=3$, $2x^2 + y^2 = 5$ be solved using matrices?
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The answer to your question is NO as this system is not a linear one. However, if you try to solve this system graphically, you can see that the ellipse $2x^2$+$y^2$=$5$ lies completely inside the line $x+y$=$3$. They never intersect each other thereby suggesting no solution in Real plane.