Question

4 Rezolvați prin metoda substituției:a) 2(x + y +1) - 3(2x - y - 3)=12 a) 4(2x - y -1)+3(3 - x - y)=3 b) √2•x+√5•y=7 b)5.x-√2•y=0 c) x +3/ y-1
x/y-8
X-4• y=6
vă rog mult.​
urgent

Answer 1

Răspuns:

a.

$x = 1 \\ y = 1$

b.

$x = \frac{7 \sqrt{2}(5 \sqrt{5} - 2) }{121} \\ y = \frac{35(5 \sqrt{5} - 2 }{121}$

Explicație pas cu pas:

a.

$2x + 2y + 2 - 6x + 3y + 9 = 12 \\ - 4x + 5y = 1 \\ x = \frac{5y - 1}{4} \\ 8x - 4y - 4 + 9 - 3x - 3y = 3 \\ 5x - 7y = - 2 \\ 5 \times \frac{5y - 1}{4} - 7y = - 2 \\ 25y - 5 - 28y = - 8 \\ 3y = 3 \\ y = 1 \\ x = \frac{5 \times 1 - 1}{4} = \frac{4}{4} \\ x = 1$

b.

$\sqrt{2} x + \sqrt{5} y = 7 \\ x = \frac{7 - \sqrt{5}y }{ \sqrt{2} } \\ 5x - \sqrt{2} y = 0 \\ 5 \times \frac{7 - \sqrt{5} y}{ \sqrt{2} } - \sqrt{2} y = 0 \\ 35 - 5 \sqrt{5} y - 2y = 0 \\ (5 \sqrt{5} + 2)y = 35 \\ y = \frac{35}{5 \sqrt{5} + 2 } = \frac{35(5 \sqrt{5} - 2)}{(5 \sqrt{5} + 2)(5 \sqrt{5} - 2)} \\ y= \frac{35(5 \sqrt{5 } - 2)}{121} \\ \sqrt{2}x + \sqrt{5} \times \frac{35(5 \sqrt{5} - 2) }{121} = 7 \\ x = \frac{7 \sqrt{2}(5 \sqrt{5} - 2) }{121}$

c.