Question 868572
{{{3x+2y=10}}}
{{{2y=10-3x}}}
{{{y=5-(3/2)x}}}
Substitute,
{{{x^2-xy+y^2=21}}}
{{{x^2-x(5-(3/2)x)+(5-(3/2)x)^2=21}}}
{{{x^2-5x+(3/2)x^2+(25-15x+(9/4)x^2)=21}}}
{{{(19/4)x^2-20x+25=21}}}
{{{(19/4)x^2-20x+4=0}}}
{{{19x^2-80x+16=0}}}
{{{(x-4)(19x-4)=0}}}
Two solutions:
{{{x-4=0}}}
{{{x=4}}}
Then,
{{{y=5-(3/2)4}}}
{{{y=5-6}}}
{{{y=-1}}}
and
{{{19x-4=0}}}
{{{19x=4}}}
{{{x=4/19}}}
Then,
{{{y=5-(3/2)(4/19)}}}
{{{y=5-6/19}}}
{{{y=89/19}}}