Question 1142955
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(1) {{{4x^2-9y^2 = 19}}}
(2) {{{2x+3y = 1}}}<br>
Rewrite (1) by factoring the left had side:
(3) {{{(2x+3y)(2x-3y) = 19}}}<br>
Use (2) and (3) to conclude that
(4) {{{2x-3y = 19}}}<br>
Add (2) and (4):
{{{4x = 20}}}
(5) {{{x = 5}}}<br>
Substitute (5) in (2):
{{{10+3y = 1}}}
{{{3y = -9}}}
{{{y = -3}}}<br>
ANSWER: (x,y) = (5,-3)<br>
CHECK: {{{4x^2-9y^2 = 4(25)-9(9) = 100-81 = 19}}}