Răspuns:
Explicație pas cu pas:
a)
[tex]x + \sqrt{2} * y = 3[/tex]
[tex]x = 3 - \sqrt{2} * y[/tex]
[tex]4 * x - 2 * \sqrt{2} * y = 12[/tex]
[tex]4 * (3 - \sqrt{2} * y) - 2 * \sqrt{2} * y = 12[/tex]
[tex]12 - 4 * \sqrt{2} * y - 2 * \sqrt{2} * y = 12[/tex]
[tex]-6 * \sqrt{2} * y = 12 - 12\\-6 * \sqrt{2} * y = 0[/tex]
y = 0
[tex]x = 3 - \sqrt{2} * y[/tex]
[tex]x = 3 - \sqrt{2} * 0\\x = 3[/tex]
b)
[tex]\sqrt{3} * x + y = 1 - 2 * \sqrt{3} \\y = 1 - 2 * \sqrt{3} - \sqrt{3} * x[/tex]
[tex]\sqrt{12} * x - 2 * y = -\sqrt{48} - 2\\\\\sqrt{4 * 3} * x - 2 * y = -\sqrt{16 * 3} - 2\\\\2 * \sqrt{3} * x - 2 * y = -4 * \sqrt{3} - 2\\\\2 * \sqrt{3} * x - 2 * (1 - 2 * \sqrt{3} - \sqrt{3} * x ) = -4 * \sqrt{3} - 2\\\\2 * \sqrt{3} * x - 2 + 4 * \sqrt{3} + 2 * \sqrt{3} * x = -4 * \sqrt{3} - 2\\\\4 * \sqrt{3} * x = -4 * \sqrt{3} - 2 + 2 - 4 * \sqrt{3}\\\\4 * \sqrt{3} * x = -8 * \sqrt{3}\\\\4 * x = -8\\\\x = -8 : 4 \\\\x = -2[/tex]
c)
[tex]\sqrt{5} * x + 5 * y = -25\\\\5 * y = -25 - \sqrt{5} * x\\\\y = \frac{-25 - \sqrt{5} * x}{5} \\\\\sqrt{20} * x - 3 * y = 15\\\\\sqrt{4 * 5} * x - 3 * y = 15\\\\2 * \sqrt{5} * x - 3 * y = 15\\\\2 * \sqrt{5} * x - 3 * \frac{-25 - \sqrt{5} * x }{5} = 15[/tex]
[tex]2 * \sqrt{5} * x + \frac{75 + 3 * \sqrt{5} * x}{5} = 15[/tex]
Inmultim tot randul anterior cu 5
[tex]5 * 2 * \sqrt{5} * x + 5 * \frac{75 + 3 * \sqrt{5} * x}{5} = 5* 15[/tex]
[tex]10 * \sqrt{5} * x + 75 + 3 * \sqrt{5} * x = 75\\\\13 * \sqrt{5} * x = 75 - 75\\\\13 * \sqrt{5} * x = 0\\\\x = 0\\[/tex]
[tex]y = \frac{-25 - \sqrt{5} * x}{5} \\\\y = \frac{-25 - \sqrt{5} * 0}{5} \\\\y = \frac{-25}{5} \\\\y = -5[/tex]
d)
[tex]\sqrt{2} * x + 3 * y = 8\\\\3 * y = 8 - \sqrt{2} * x\\\\y = \frac{8 - \sqrt{2} * x}{3} \\\\-\sqrt{50} * x + 6 * y = 2\\\\\-\sqrt{25 * 2} * x + 6 * y = 2\\\\-5 * \sqrt{2} * x + 6 * y = 2\\\\-5 * \sqrt{2} * x + 6 * \frac{8 - \sqrt{2} * x }{3} = 2\\\\-5 * \sqrt{2} * x + 2 * (8 - \sqrt{2} * x) = 2\\\\-5 * \sqrt{2} * x + 16 - 2 * \sqrt{2} * x = 2\\\\-7 * \sqrt{2} * x = 2 - 16\\\\-7 * \sqrt{2} * x = -14\\\\\sqrt{2} * x = \frac{-14}{-7} \\\\\sqrt{2} * x = -2\\\\[/tex]
[tex]x = \frac{-2}{\sqrt{2}}[/tex]
[tex]y = \frac{8 - \sqrt{2} * x }{3} \\[/tex]
[tex]y = \frac{8 - \sqrt{2} * \frac{-2}{\sqrt{2} } }{3} \\[/tex]
[tex]y = \frac{8 - (-2)}{3} \\\\y = \frac{8 + 2}{3} \\\\y = \frac{10}{3} \\[/tex]
