Вправа 6.77 гдз 7 клас алгебра Біляніна Білянін Андрух

№ 6.77
Увідповіднити систему рівнянь $(1-4)$ і суму $\mathrm{x}_0+\mathrm{y}_0(\mathrm{~A}-$ Д) її розв'язків ( $\mathrm{x}_0 ; \mathrm{y}_0$ ): $$
\begin{aligned}
& \text { 1. }\left\{\begin{array}{l}
4 \cdot(x+y)-5 \cdot(x-y)=15 \\
5 \cdot(x+y)-4 \cdot(x-y)=21
\end{array}\right. \\
& \left\{\begin{array}{l}
4 x+4 y-5 x+5 y=15 \\
5 x+5 y-4 x+4 y=21
\end{array}\right. \\
& \left\{\begin{array}{l}
-x+9 y=15 \\
x+9 y=21
\end{array}\right.
\end{aligned}
$$
–х + 9у + х + 9у = 15 + 21,
18у = 36,
у = 2.
х = 21 – 9 • 2 = 3,
х₀ + у₀ = 3 + 2 = 5. В
\begin{aligned}
& \text { 2. }\left\{\begin{array}{l}
8+5 x=3 \cdot(4-y) \\
5-(2 x+3)=4 y-8
\end{array}\right. \\
& \left\{\begin{array}{l}
8+5 y=12-3 y \\
5-2 x-3=4 y-8
\end{array}\right. \\
& \left\{\begin{array}{l}
5 x+3 y=12-8 \\
-2 x-4 y+-8-2
\end{array}\right. \\
& \left\{\begin{array}{l}
5 x+3 y=4, / \cdot 2 \\
-2 x-4 y=-10, / \cdot 5
\end{array}\right. \\
& \left\{\begin{array}{l}
10 x+6 y=8 \\
-10 x-20 y=-50
\end{array}\right.
\end{aligned}
–14у = –42,
у = 3,
5х = 4 – 3у,
5х = 4 – 3 • 3,
5х = –5,
х = –1,
х₀ + у₀ = –1 + 3 = 2. А
\begin{aligned}
& \text { 3. }\left\{\begin{array}{l}
4-2 x=4 \cdot(2 y+5) \\
5 \cdot(x+y)=-10
\end{array}\right. \\
& \left\{\begin{array}{l}
4-2 x=8 y+20 \\
5 x+5 y=-10
\end{array}\right. \\
& \left\{\begin{array}{l}
-2 x-8 y=20-4 \\
5 x+5 y=-10, /: 5
\end{array}\right. \\
& \left\{\begin{array}{l}
-2 x-8 y=16, /: 2 \\
x+y=-2,
\end{array}\right. \\
& \left\{\begin{array}{l}
-x-4 y=8 \\
x+y=-2
\end{array}\right.
\end{aligned}
–х – 4у + х + у = 8 – 2,
–3у = 6,
у = –2,
х = –2 – у,
х = –2 + 2 = 0,
х₀ + у₀ = 0 – 2 = –2. Д
\begin{aligned}
& \text { 4. }\left\{\begin{array}{l}
3 \cdot(x-6)=4 x-10 y \\
6 x-7=2 \cdot(y-2)+5
\end{array}\right. \\
& \left\{\begin{array}{l}
3 x-18=4 x-10 y \\
6 x-7=2 y-4+5
\end{array}\right. \\
& \left\{\begin{array}{l}
3 x-4 x+10 y=18 \\
6 x-2 y=1+7,
\end{array}\right. \\
& \left\{\begin{array}{l}
-x+10 y=18, / \cdot 6 \\
6 x-2 y=8
\end{array}\right. \\
& \left\{\begin{array}{l}
-6 x+60 y=108 \\
6 x-2 y=8
\end{array}\right.
\end{aligned}
60у – 2у = 108 + 8,
58у = 116,
у = 2,
х = 10у – 18,
х = 10 • 2 – 18 = 2,
х₀ + у₀ = 2 + 2 = 4. Б
Відповідь: 1 – В, 2 – А, 3 – Д, 4 – Б.