Вправа 6.41 гдз 7 клас алгебра Біляніна Білянін Андрух

№ 6.41
Знайти розв’язок системи рівнянь, використовуючи спосіб
підстановки: $$
\begin{aligned}
& \text { a) }\left\{\begin{array}{l}
3 x+4 y=-13 \\
2 x-5 y=22
\end{array}\right. \\
& \left\{\begin{array}{l}
3 x+4 y=-13 \\
2 x=22+5 y
\end{array}\right. \\
& \left\{\begin{array}{l}
3 \cdot(11+2,5 y)+4 y=-13 \\
x=11+2,5 y
\end{array}\right. \\
& \left\{\begin{array}{l}
33+7,5 y+4 y=-13 \\
x=11+2,5 y
\end{array}\right. \\
& \left\{\begin{array}{l}
11,5 y=-46, \\
x=11+2,5 y
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-4 \\
x=11+2,5 \cdot(-4)
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-4 \\
x=1
\end{array}\right.
\end{aligned}
$$
$$
\text { б) }\left\{\begin{array}{l}
x-y=10 \\
2 x-3 y=27
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x=10+y \\
2 \cdot(10+y)-3 y=27
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x=10+y \\
20+2 y-3 y=27
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x=10+y \\
-y=7
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x=10-7 \\
y=-7
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x=3 \\
y=-7
\end{array}\right.
$$
$$
\begin{aligned}
& \text { в) }\left\{\begin{array}{l}
x-3 y=-14 \\
4 x+5 y=12
\end{array}\right. \\
& \left\{\begin{array}{l}
x=-14+3 y \\
4 \cdot(-14+3 y)+5 y=12
\end{array}\right.
\end{aligned}
$$
\begin{aligned}
&\begin{aligned}
& \left\{\begin{array}{l}
x=-14+3 y, \\
-56+12 y+5 y=12
\end{array}\right. \\
& \left\{\begin{array}{l}
x=-14+3 y \\
17 y=68
\end{array}\right. \\
& \left\{\begin{array}{l}
x=-14+3 \cdot 4 \\
y=4
\end{array}\right. \\
& \left\{\begin{array}{l}
x=-2 \\
y=4
\end{array}\right.
\end{aligned}\\
&\begin{aligned}
& \text { г) }\left\{\begin{array}{l}
2 x+y=-13 \\
5 x-2 y=-19
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-2 x-13 \\
5 x-2 \cdot(-2 x-13)=-19
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-2 x-13 \\
5 x+4 x+26=-19
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-2 x-13 \\
9 x=-45
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-2 \cdot(-5)-13 \\
x=-5
\end{array}\right. \\
& \left\{\begin{array}{l}
y=-3 \\
x=-5
\end{array}\right.
\end{aligned}\\
&\text { Відповідь: а) }(1 ;-4), \text { б) }(3 ;-7) \text {, в) }(-2 ; 4), \text { г) }(-5 ;-3) \text {. }
\end{aligned}