讲解一下二元一次方程组---Here's the extracted content from the image:
**1. Textual Information:**
* **Phone Status Bar:**
* Time: 13:31
* Network indicators: Wi-Fi, 5G (twice, indicating signal strength), 4G/LTE signal strength bars.
* Battery: 72%
* **Message Header:**
* Sender/Recipient Number: 121233205
* **Message Details:**
* Sender Indicator: 1 (likely representing the first message in a thread or an unread count)
* Message Timestamp: 13:30
* **Message Content:**
【苏州交警】您的小型汽车苏ES72A2检验有效期至2025年10月31日，属于非免检车辆，请按时办理定期检验业务，您应当前往安全技术检验机构检验并申领检验合格标志。未经检验合格的机动车，不得上道路行驶！如已办理业务，请忽略此消息。友情提醒：安全技术检验机构可以通过“交管12123”APP查询。如您存在违法、发生交通事故未造成人员伤亡等情况，请您处理完成后再申领检验合格标志。
*Translation of Message Content:*
【Suzhou Traffic Police】Your small car Su ES72A2's inspection validity period is until October 31, 2025. It is a non-exempt vehicle, please handle the regular inspection business on time. You should go to a safety technical inspection agency for inspection and apply for an inspection qualification mark. Motor vehicles that have not passed the inspection are not allowed to drive on the road! If you have already processed the business, please ignore this message. Friendly reminder: Safety technical inspection agencies can be inquired through the "Traffic Management 12123" APP. If you have violations, or have been involved in traffic accidents that did not cause casualties, please apply for the inspection qualification mark after completing the resolution.
* **Bottom Input Bar:**
* Text Input Field Placeholder: 短信 (SMS)
* Unread Message Indicator: 1
**2. Chart/Diagram Description:**
The image is a screenshot of a mobile phone's messaging interface.
* **Top Bar (Status Bar):** Displays current time (13:31), network status (Wi-Fi, 5G, signal strength), and battery percentage (72).
* **Header Bar:** Contains a back arrow icon on the left, the contact number "121233205" in the center, and a vertical ellipsis (more options) icon on the right.
* **Message Area:** Contains a single message bubble from the sender.
* To the left of the message bubble, there is a small circle with the number "1" inside, and below it, the message timestamp "13:30".
* The message content is a multi-paragraph text block from "苏州交警" (Suzhou Traffic Police). It is an alert regarding a vehicle inspection due date (October 31, 2025) for vehicle "苏ES72A2", instructing the recipient to complete the inspection and apply for a qualification mark. It also provides warnings, reminders to check via "交管12123" APP, and instructions for cases with violations or accidents. The date "2025年10月31日" and the text "交管12123" are underlined, indicating they might be clickable links or interactive elements.
* **Bottom Input Bar:** Located at the bottom of the screen.
* On the left, there is a plus sign (+) icon, typically for attaching media or other content.
* In the center, there is a text input field labeled "短信" (SMS).
* On the right, there is an arrow pointing upwards, likely the send button. There is also a small blue square with the number "1" inside, possibly indicating an unread message count or a draft message count.
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A system of linear equations consists of two or more linear equations with the same variables. In this example, we have two equations: x plus y equals two, and y equals one-half x plus one. We can solve such systems by finding the point where the lines intersect.
To solve a system of linear equations graphically, we plot each equation on the same coordinate plane. The solution is the point where all lines intersect. In this case, the two lines intersect at the point two-thirds, four-thirds. This means that x equals two-thirds and y equals four-thirds is the solution to our system of equations.
Besides graphical methods, we can also solve systems algebraically. One common method is substitution. Let's see how it works with our example equations. First, we have x plus y equals two and y equals one-half x plus one. We substitute the expression for y from the second equation into the first equation. This gives us x plus one-half x plus one equals two. Combining like terms, we get three-halves x plus one equals two. Subtracting one from both sides, we have three-halves x equals one. Finally, solving for x, we find x equals two-thirds. Substituting this value back into the second equation, we find y equals four-thirds.
Another algebraic method is elimination. We add or subtract equations to eliminate one variable. Let's apply this method to our system. First, we have x plus y equals two and y equals one-half x plus one. We rewrite the second equation as negative one-half x plus y equals one. Now we multiply the first equation by one-half to get one-half x plus one-half y equals one. We subtract the second equation from this modified first equation to eliminate x. This gives us one-half x plus one-half y minus negative one-half x plus y equals one minus one. Simplifying, we get three-halves y equals zero, which means y equals four-thirds. Finally, we substitute this value back into the first equation to find x equals two-thirds.
Systems of linear equations can have different types of solutions. Let's explore the three main cases with graphical examples. Case one: The lines intersect at exactly one point. This system has one unique solution. Case two: The lines are parallel and never intersect. This system has no solution. Case three: The lines are identical and overlap completely. This system has infinitely many solutions.