Question 972410

Hello! I need help on solving these systems of equations, quadratic

{{{9y^2+77x-190=0}}},
{{{14x^2-9y^2-7x-6=0}}}
<pre>      {{{9y^2 + 77x - 190 =0 }}} ---- eq (i)
{{{14x^2 - 9y^2 -  7x - 6 = 0}}} ------- eq (ii)
{{{14x^2 + 70x - 196 = 0}}} ------- Adding eqs (ii) & (i)
{{{14(x^2 + 5x - 14) = 14(0)}}}
{{{x^2 + 5x - 14 = 0}}}
(x + 7)(x - 2) = 0
x + 7 = 0          OR        x - 2 = 0
{{{highlight_green(system(x = - 7_or,x = 2))}}}

If x = - 7
{{{9y^2 + 77x - 190 = 0}}} ---- eq (i)
{{{9y^2 + 77(- 7) - 190 = 0}}}
{{{9y^2 - 539 - 190 = 0}}}
{{{9y^2 -  729 = 0}}}
{{{9(y^2 - 81) = 9(0)}}}
{{{y^2 = 81}}}
{{{highlight_green(system(y = 9_or,y = - 9))}}}
Thus, we get: {{{highlight_green(system(when_x = 7,y = 0_or, y = - 7))}}}
If x = 2
{{{9y^2 + 77x - 190 = 0}}} ---- eq (i)
{{{9y^2 + 77(2) - 190 = 0}}}
{{{9y^2 + 154 - 190 = 0}}}
{{{9y^2 -  36 = 0}}}
{{{9(y^2 - 4) = 9(0)}}}
{{{y^2 = 4}}}
{{{highlight_green(system(y = 2_or,y = - 2))}}}
Thus, we get: {{{highlight_green(system(when_x = 2,y = 2_or, y = - 2))}}}