Answer:
[tex]x = \frac{57}{29} \ , \ y = \frac{12}{29}[/tex]
Step-by-step explanation:
2x + 5y = 6 --------( 1 )
5x - 2y = 9 --------( 2 )
_____________
( 1 ) x 5 => 10x + 25y = 30 -----------( 3 )
( 2 ) x 2 => 10x - 4y = 18 ----------- ( 4 )
______________
( 3 ) - ( 4 ) => 0 + 29y = 12
[tex]y = \frac{12}{29}[/tex]
Substitute y in ( 1 ) =>
[tex]2x + (5 \times \frac{12}{29}) = 6\\\\2x + \frac{60}{29} = 6\\\\2x = 6 - \frac{60}{29}\\\\2x = \frac{174 - 60}{29}\\\\x = \frac{114}{29 \times 2}\\\\x = \frac{57}{29}[/tex]
