3x+2y=13 and xy=2

Question

Simultaneous equations

One quadratic and one linear 

Answer 1

3x+2y=13

xy=2

From the second equation y=2/x, (x≠0) and substitute into the first one

3x+2(2/x)=13

3x²-13x+4=0

x=1/3, x=4

y=2/(1/3)=6, and y=1/4

So, there two pairs of solutions: (1/3, 6) and (4, 1/4).