Question

1.Rezolvati ecuatia x radical din 3-1=5
2. Rezolvati sistemul x+y=3
3x-2y=4

Answer 1

$1)x \sqrt{3} - 1 = 5$

$x \sqrt{3} = 5 + 1$

$x \sqrt{3} = 6$

$x = \frac{6}{ \sqrt{3} }$

$x = \frac{6 \sqrt{3} }{3}$

$x = 2 \sqrt{3}$

2)I) Metoda substituției :

$\left\{\begin{matrix} x + y = 3\\ 3x - 2y = 4\end{matrix}\right.$

$x + y = 3$

$x = 3 - y$

$3x - 2y = 4$

$3(3 - y) - 2y = 4$

$9 - 3y - 2y= 4$

$- 3y - 2y = 4 - 9$

$- 5y = - 5 \: | \div ( - 5)$

$y = 1$

$x = 3 - y$

$x = 3 - 1$

$x = 2$

II) Metoda reducerii :

$\left\{\begin{matrix} x + y = 3 \: | \times 2 \\ 3x - 2y = 4\end{matrix}\right.$

$\left\{\begin{matrix} 2x + 2y = 6\\ 3x - 2y = 4\end{matrix}\right.$

$2x + 3x + 2y - 2y = 6 + 4$

$5x = 10 \: | \div 5$

$x = 2$

$x + y = 3$

$2 + y = 3$

$y = 3 - 2$

$y = 1$

Answer 2

a) x√3-1=5
x√3=5+1
x√3=6
x=6/√3
x=6√3/3
x=2√3

b) x+y=3  ⇒  x=3-y
3(3-y)-2y=4
9-3y-2y=4
9-5y=4
-5y= 4-9
y=5/5
y=1
x=3-1
x=2

S(2; 1)