[tex]\text{Prin metoda substitutiei: } \\1)\\x = 5 \\ 3x +7y=11 \\ \\ x = 5\;\;\;\;\text{(este substitutie) } \\ 3*5+7y=11 \\ 7y=11-3*5 \\ 7y= 11-15\\7y=-4\\y= \frac{-4}{7} \\ Solutia: \\ x=\boxed{5} \\y= \boxed{\frac{-4}{7} }[/tex]
[tex]2) \\ x=4y \\ 3x+5y-15=0 \\ x=4y\;\;\;\;\;\text{este substitutie} \\ 3*(4y)+5y=15 \\ 12y+5y=15\\17y=15\\y= \boxed{\frac{15}{17}}\\x=4y=4*\frac{15}{17}= \boxed{\frac{60}{17}}[/tex]
[tex]\text{Prin metoda reducerii: } \\ \\ a) \\ 9x+11y=15\\7x+11y=19 \\ \text{--------------------- scadem ecuatiile } \\ 2x\;\;\;\;\;\;\;\text{/}\;=-4 \\ x= \frac{-4}{2}=\boxed{-2} \\ 9*(-2)+11y=15 \\ -18+11y=15 \\ 11y=15+18 \\ 11y=33 \\ y= \frac{33}{11} =\boxed{3}[/tex]
[tex]b) \\ 4x+y=7 \;\;\;\;\;\;|\;*(-2)\\ 9x+2y=63 \\ ....... \\ -8x-2y=-14\\ 9x+2y=63 \\ \text{----------------------- adunam ecuatiile} \\ x = \boxed{49} \\ 9*49 + 2y = 63 \\441 + 2y = 63 \\2y=63-441 \\ 2y=-378 \\y= \frac{-378}{2} =\boxed{-189}[/tex]
[tex]c) \\ 3x+5y=11\;\;\;\;|\;*3 \\ 4x-3y=-9\;\;\;\;|\;*5 \\ 9x+15y=33 \\ 20x-15x=-45 \\ \text{--------------------- adunam ecuatiile } \\ 29x= -12 \\ x= \boxed{\frac{-12}{29}} \\ 3*\frac{-12}{29}+5y=11 \\ \frac{-36}{29} +5y=11 \\ 5y=11-\frac{-36}{29} \\ 5y= \frac{29*11+\;\;\;36}{29} \\ 5y= \frac{355}{29} \\ y=\frac{355}{29*5}=\boxed{\frac{71}{29}}[/tex]
[tex]d) \\ 13x+12y=8 \\ 7x+12y=14 \\ \text{--------------------- scadem ecuatiile } \\ 6x=-6 \\ x= \frac{-6}{6} =\boxed {-1} \\ 7*(-1)+12y=14 \\ -7+12y=14 \\ 12y=14+7 \\ 12y=21 \\ y= \frac{21}{12} =\boxed{ \frac{7}{4}}[/tex]
