Вправи: 1094

1094. Знайди розв’язок системи рівнянь.

а) 4(x – 3z) + 33z = 50;

5(x + 2z) – 3z = 18;

4x – 12z + 33z = 50;

5x + 10z – 3z = 18;

4x + 21z = 50;

2x + 10z = 18;

2x = 18 – 10z;

2(18 – 10z) + 21z = 50;

36 – 20z + 21z = 50;

z = 50 – 36;

z = 14;

2x = 18 – 10 • 14 = 18 – 140 = –122;

x = –61.

Відповідь: (–61; 14).

б) 4x + 7 = 5(x + t);

3(x + 5y) – 6t = 15;

4x + 7 = 5x + 5t;

3x + 15t – 6t = 15;

4x – 5x – 5t = –7;

3x + 9t = 15;

–x – 5t = –7|: (–1);

3x + 9t = 15|: 3;

x + 5t = 7;

x + 3t = 5;

x = 7 – 5t;

7 – 5t + 3t = 5;

–2t = 5 – 7;

–2t = –2;

t = 1;

x = 7 – 5 • = 2.

Відповідь: (2; 1).