rozwiąz układ rownań

[kiinja]

1.
\(\begin{cases} 12x+15y=8 \\ 16x+9y=7 \end{cases}\)

2.
\(\begin{cases} -8x+2y=13 \\ 3x-y=6 \end{cases}\)

[domino21]

zad 1.

\(\begin{cases} 12x+15y=8 \\ 16x+9y=7 \ | \ \cdot \ (- \frac{3}{4}) \end{cases} \ \Rightarrow \begin{cases} 12x+15y=8 \\ -12x-\frac{27}{4}y =-\frac{21}{4} \end{cases} \ \Rightarrow \ 12x -12x +15y -\frac{27}{4}y =8-\frac{21}{4} \ \Rightarrow \\ \Rightarrow \ \frac{33}{4}y =\frac{11}{4} \ \Rightarrow \ y=\frac{1}{3}\)

\(12x+15y=8 \ \wedge \ y=\frac{1}{3} \ \Rightarrow \ 12x+15\cdot \frac{1}{3} =8 \ \Rightarrow \ 12x =3 \ \Rightarrow \ x =\frac{1}{4}\)

odp: \(\ \begin{cases} x =\frac{1}{4} \\ y=\frac{1}{3} \end{cases}\)

[domino21]

zad 2.

\(\begin{cases} -8x+2y=13 \\ 3x-y=6 \ \Rightarrow \ y=3x-6 \end{cases}\)

\(-8x+2(3x-6)=13 \ \Rightarrow \ -8x+6x-12=13 \ \Rightarrow \ -2x=25 \ \Rightarrow \ x=-\frac{25}{2}\)

\(y=3x-6 \ \Rightarrow \ y=3\cdot (-\frac{25}{2}) -6 =-\frac{75}{2}-6=-\frac{87}{2}\)