Question

folosind metoda reducerii
5x-4y=-23
7x+6y=-9

Answer 1

5x-4y=-23I6(inmultim cu 6)
7x+6y=-9I4(inmultim cu 4)
30x-24y=-138
28x+24y=-36    apoi adunam membru cu membru
58x=-174, rezulta x=-174/58=-3
rezulta y=(-9-7x)/6=(-9+21)/6=12/6=2

Answer 2

$\displaystyle \left \{ {{5x-4y=-23| \cdot 3} \atop {7x+6y=-9| \cdot 2}} \right. \Rightarrow \left \{ {{15x-12y=-69} \atop {14x+12y=-18}} \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~--------- \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~29x~~~~~/~~=-87 \Rightarrow x=- \frac{87}{29} \Rightarrow \boxed{x=-3} \\ \\ 5x-4y=-23 \Rightarrow 5 \cdot (-3)-4y=-23 \Rightarrow -15-4y=-23 \Rightarrow \\ \\ \Rightarrow -4y=-23+15 \Rightarrow -4y=-8 \Rightarrow y= \frac{8}{4} \Rightarrow \boxed{y=2}$