Question 30000
[1] {{{4*x^2 + 9*y^2= 36}}}
[2] {{{y = x+3}}}
Substitute {{{y = x+3}}} in [1]
{{{4*x^2 + 9*(x + 3)^2 = 36}}}
{{{4*x^2 + 9*(x^2 + 6*x + 9) = 36}}}
{{{4*x^2 + 9*x^2 + 54*x + 81 = 36}}}
{{{13*x^2 + 54*x + 45 = 0}}}
use
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-54 +- sqrt( 54^2-4*13*45 ))/(2*13) }}}
{{{x = (-54 +- sqrt( 2916-2340 ))/(26)}}}
{{{x = (-54 +- sqrt( 576 ))/(26)}}}
{{{x = (-54 +- 24)/(26)}}}
{{{x = (-27 +- 12)/(13)}}}
[3] {{{x = -15/13}}}
[4] {{{x = -3}}}
substitute [3] in [2]
{{{y = -15/13 + 3}}}
{{{y = -15/13 + 39/13}}}
{{{y = 24/13}}}
[5] (-15/13 , 24/13) is one solution
substitute [4] in [2]
{{{y = -3 + 3}}}
{{{y = 0}}}
[6] (-3 , 0) is the other solution
check [5] in [1]
{{{4*(-15/13)^2 + 9*(24/13)^2= 36}}}
{{{4*(-15/13)^2 + 9*(24/13)^2= 36}}}
Multiply both sides by 13^2
{{{4*(-15)^2 + 9*(24)^2= 36 * 13^2}}}
{{{4 * 225 + 9 * 576 = 6084}}}
{{{900 + 5184 = 6084}}}
{{{6084 = 6084}}}
OK
check [6] in [1]
{{{4*(-3)^2 + 9*(0)^2= 36}}}
{{{4 * 9 + 0 = 36}}}
{{{36 = 36}}}
OK