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1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

1 Primary & Middle School Biology1–9 年级在线 2 High School Biology10–12 年级在线 3 University Biology — Year 1本科一年级在线 4 University Biology — Year 2本科二年级在线 5 University Biology — Year 3本科三年级在线

1 Primary & Middle School Earth and Space Sciences1–9 年级在线 2 High School Earth and Space Sciences10–12 年级在线 3 University Earth and Space Sciences — Year 1本科一年级在线 4 University Earth and Space Sciences — Year 2本科二年级在线 5 University Earth and Space Sciences — Year 3本科三年级在线

1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Mathematics · 术语表

什么是 Linear system？

Definition 7.7 High School Mathematics · 第 7 章 — Equations of Lines and Linear Systems

A system of two linear equations in the unknowns $x$ and $y$ is a pair of equations

\begin{cases} a x + b y = c \\ a' x + b' y = c' \end{cases}

to be satisfied simultaneously. A solution is a pair $(x, y)$ satisfying both. Each equation describes a line, so solving the system means finding the intersection of two lines.

A linear system seen geometrically: each equation is a line, and the solution (2,1) of is their intersection point. — A linear system seen geometrically: each equation is a line, and the solution $(2,1)$ of Example 7.11 is their intersection point.

示例

Example 7.13 (Modeling with a system)

Three notebooks and two pens cost $8$ ; one notebook and four pens cost $6$ . Let $x$ be the price of a notebook and $y$ that of a pen:

\begin{cases} 3x + 2y = 8 \\ x + 4y = 6 . \end{cases}

From the second equation, $x = 6 - 4y$ ; substituting, $3(6 - 4y) + 2y = 8$ , so $18 - 10y = 8$ , giving $y = 1$ and then $x = 2$ . A notebook costs $2$ and a pen costs $1$ .

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