Hệ có nghiệm là

15/24

Hệ \(\left\{ {\begin{array}{*{20}{c}}{x - y = 5}\\{{x^2} - {y^2} = 15}\end{array}} \right.\) có nghiệm là

\[x = - 1;y = 4\]

\[x = 4;y = - 1\]

\[x = - 1;y = - 1\]

\[x = 4;y = 4\]

Giải thích

Cách 1:

\(\left\{ {\begin{array}{*{20}{c}}{x - y = 5}\\{{x^2} - {y^2} = 15}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{y = x - 5}\\{{x^2} - {{(x - 5)}^2} = 15}\end{array}} \right.\)

\(\left\{ {\begin{array}{*{20}{c}}{y = x - 5}\\{10x - 25 = 15}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{y = x - 5}\\{x = 4}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{y = - 1}\\{x = 4}\end{array}} \right.\)

Cách 2

\(\left\{ {\begin{array}{*{20}{c}}{x - y = 5}\\{{x^2} - {y^2} = 15}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{x - y = 5}\\{x + y = 3}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{x = 4}\\{y = - 1}\end{array}} \right.\)

Đáp án cần chọn là: B