Решите систему { x + y + z = 5 2x - y + z = 2 3x - 2y + z = 1

Question

Решите систему
{ x + y + z = 5
2x - y + z = 2
3x - 2y + z = 1

Answer 1

{х=5–y–z
{2(5–y–z)–y+z=2
{3(5–y–z)–2y+z=1
{10–2y–2z–y+z=2
{15–3y–3z–2y+z=1
{–3y–z=–8
{–5y–2z=–14
{z=8–3y
{–5y–2(8–3y)=–14
–5y–16+6y=–14
y=2
z=8–3•2=2
x=5–2–2=1
Ответ: (1;2;2)

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