Відповіді на вправи: 523 (1-2)

1) x + y = 1;

y + z = 2;

xz = 6;

x = 1 – y;

z = 2 – y;

(1 – y)(2 – y) = 6;

2 – y – 2y + y² – 6 = 0;

y² – 3y – 4 = 0;

y₁ = –1, y₂ = 4;

y = –1; y = 4;

x = 1 + 1; x = 1 – 4;

z = 2 + 1; z = 2 – 4;

y = –1; y = 4;

x = 2; x = –3;

z = 3; z = –2;

Відповідь: (2; –1; 3), (–3; 4; –2)

2) xy = 2;

yz = 6;

xz = 3;

xy = 2; | •.

xz = 3;

x²yz = 6;

x² = $\frac{6}{\mathrm{yz}}$;

x² = $\frac{6}{6}$;

x² = 1;

x₁ = –1, x₂ = 1.

x = –1; x = 1;

–1 • y = 2; 1 • y = 2;

–1 • z = 3; 1 • z = 3;

x = –1; x = 1;

y = –2; y = 2;

z = –3; z = 3.

Відповідь: (–1; –2; –3), (1; 2; 3)

3) x + 2y – z = 5;

3x – 4y + z = 1;

x² + y² + z² = 6;

+ x + 2y – z = 5;

3x – 4y + z = 1;

4x – 2y = 6;

4x = 6 + 2y;

x = $\frac{6+2y}{4}$;

x = $\frac{3+y}{2}$.

x + 2y – z = 5| • (–3);

3x – 4y + z = 1;

+ –3x – 6y + 3z = –15;

3x – 4y + z = 1;

–10y + 4z = –14|: 2;

–5y + 2z = –7;

2z = 5y – 7;

z = $\frac{5y-7}{2}$;

y = 1;

x = $\frac{3+1}{2}$;

z = $\frac{5•1-7}{2}$;

y = 1;

x = 2;

z = –1.

y = 1$\frac{2}{15}$;

x = $\frac{1}{2}$(3 + 1$\frac{2}{15}$);

z = $\frac{1}{2}$(5 • 1$\frac{2}{15}$ – 7);

y = 1$\frac{2}{15}$;

x = 2$\frac{1}{15}$;

z = –$\frac{2}{3}$.

+ xy + xz = 8;

yz + xy = 9;

2xy + xz + yz = 17;

2xy – 7 = 17;

2xy = 24;

xy = 12.

+ yz + xy = 9;

xz + yz = –7;

2yz + xy + xz = 2;

2yz + 8 = 2;

2yz = –6;

yz = –3.

x = –4;

y = $\frac{12}{-4}$;

z = $\frac{-4}{-4}$;

x = 4;

y = $\frac{12}{4}$;

z = $\frac{-4}{4}$;

x = –4;

y = –3;

z = 1;

x = 4;

y = 3;

z = –1.