a)3x-3+2y+8=24 ⇒ 3x+2y=19 ⇒
3y+3+x=x²-1-2x x²-3x-3y=4⇒y=[tex] \frac{4- x^{2} +3x}{-3} [/tex]
⇒3x+2×[tex] \frac{4- x^{2} +3x}{-3} [/tex]=19
Aducem la acelasi numitor
-9x+8-2x²+6x=-57
-2x²-3x+65=0
Δ=9+8×65=529
x₁,₂=[tex] \frac{3+/-23}{-4} [/tex]
x₁=[tex] \frac{-13}{2} [/tex]
x₂=5
Pentru x₁=[tex] \frac{-13}{2} [/tex]⇒y₁=[tex] \frac{4- (\frac{-13}{2}) ^{2} +3* (\frac{-13}{2}) }{-3}= \frac{4- \frac{169}{4}- \frac{39}{2} }{-3}= \frac{ \frac{16-169-78}{4} }{-3} = \\ = \frac{ \frac{-231}{4} }{-3}= \frac{-231}{4}* \frac{1}{-3}= \frac{77}{4} [/tex]
Pentru x₂=5⇒y₂=[tex] \frac{4-25+15}{-3}= \frac{-6}{-3}=2 [/tex]
b)3x+9-2y-10=1 ⇒3x-2y=2 ⇒ x=[tex] \frac{2+2y}{3} [/tex]
xy-5x+3y-15=xy-7x+8 2x+3y=23 2×[tex] \frac {2+2y{3}+3y =23 [/tex]
Aducem la acelasi numitor
4+4y+9y=69
13y=65
y=5
Pentru y=5 ⇒x=[tex] \frac{2+2*5}{3}= \frac{12}{3}=4 [/tex]
c)6x-9+15+3y=15 ⇒ 6x+3y=9 ⇒ y=[tex] \frac{9-6x}{3} [/tex]
20x-15-2y-6=3 20x-2y=24 20x-2([tex] \frac{9-6x}{3}[/tex])=24
Aducem la acelasi numitor
60x-18+12x=72
72x=72+18
72x=90
x=[tex] \frac{90}{72} [/tex]
x=[tex] \frac{45}{36}= \frac{5}{4} [/tex]
Pentru x=[tex] \frac{5}{4} [/tex]⇒y=[tex] \frac{9-6* \frac{5}{4} }{3}= \frac{ \frac{18-15}{2} }{3}= \frac{3}{4} * \frac{1}{3}= \frac{1}{4} [/tex]
d)10x+5-3y-6=3 ⇒ 10x-3y=4 ⇒10x-3y=4
4x+4y-9x-6y=-9 -5x-2y=-9 x=[tex] \frac{-9+2y}{-5} [/tex]
10×[tex] (\frac{-9+2y}{-5})-3y=4 [/tex]
2(9-2y)-3y=4
18-4y-3y=4
-7y=-14
y=2
Pentru y=2 ⇒x=[tex] \frac{-9+2*2}{-5}= \frac{-9+4}{-5}= \frac{-5}{-5}=1 [/tex]
