Question 254953
Your two equations are:
(i){{{9x^2 - 6y^2 = 291}}}
(ii){{{3x^2 + 2y^2 =197}}}
step 1 - multiply (ii) by 3 to get
(iii){{{9x^2 + 6y^2 = 591}}}
add (i) to (iii) to get
(iv) {{{18x^2 = 882}}}
solving for x, we get
{{{x^2 = 49}}}
so 
{{{x = plus or minus 7}}}
Now, find y.
{{{3*7^2 + 2y^2 =197}}}
{{{147 + 2y^2 =197}}}
{{{2y^2 = 50}}
{{{y^2 = 25}}}
{{{y = plus or minus 5}}}