Solve the simultaneous equation 2x+5y=6 and 5x-2y=9

Question

asked Feb 11, 2022 87.5k views

1 Answer

Jpnp · Answer 1 · 2022-02-15T11:22:59+0000

Answer:

$x = (57)/(29) \ , \ y = (12)/(29)$

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

y = (12)/(29)

Substitute y in ( 1 ) =>

$2x + (5 * (12)/(29)) = 6\\\\2x + (60)/(29) = 6\\\\2x = 6 - (60)/(29)\\\\2x = (174 - 60)/(29)\\\\x = (114)/(29 * 2)\\\\x = (57)/(29)$