Question

1 ) Stiind ca x+3y supra 2x+y = 23 supra 11 , calculati y supra x .

2 ) Stiind ca 3y-x supra x+y = 23 supra 13 , calculati x supra y .

3 ) Daca x supra y = 0 , ( 3 ) , calculati 5x+4y supra 3x+2y .

Answer 1

1) x+3y / 2x+y = 23/11 => 11(x+3y) = 23(2x+y) => 11x+33y=46x+23y | : x
=> 11+33y/x =46 +23y/x  => 33y/x-23y/x = 46-11 => 10 y/x =35 => y/x = 35/10=3,5
2) 13(3y-x)= 23(x+y) => 39y-13x=23x+23y | : y => 39-13x/y=23x/y+23 =>
39-23=23 x/y +13 x'y => 16= 36 x/y => x/y = 16/36= 4/9
3) x/y = 0,(3)= 3/9=1/3
x/y=1/3 => y=3x
5x+4y= 5x + 4*3x= 5x+12x=17x
3x+2y=3x+2*3x=3x+6x=9x
=> 5x +4y supra 3x+2y= 17x/9x = 17/9