这部分需要会什么？
- 用代入法或消元法解二元一次方程组
- 把交点坐标解释为同时满足两个条件的数对
- 直接求所需的组合量
核心概念与公式
方程组的解 \((x,y)\) 必须同时满足每一个方程。代入法适合某个变量已经被单独表示的情形；消元法通过倍乘、相加或相减消去一个变量。图象上，两条直线的交点就是方程组的解。
若只要求 \(x+y\)、\(2x-y\) 等组合，可以先观察能否把两个方程线性组合成目标式。这样常常比把两个未知数都求出来更快。
做题时怎样使用
- 对齐两个方程的同类项，先选最容易消掉的变量
- 消元或代入得到一个变量，再代回求另一个
- 检查两个原方程，并确认题目问的是单个变量还是组合量
容易混淆的地方
将方程乘一个数时，每一项和等号右边都要乘；两个方程相减时，要给第二个方程的整行加括号。
用一个例题串起方法
知识点教学例题已知 \(2x+y=11\)，\(x-y=1\)，求 \(x+y\)。
展开解题思路 ＋
两式相加得 \(3x=12\)，故 \(x=4\)。代入 \(x-y=1\) 得 \(y=3\)，于是 \(x+y=7\)。数对 \((4,3)\) 同时满足两个方程。
本知识点题库
先独立作答，再查看答案与解析。
二元一次方程组求解基础
A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?
原库参考解析
二元一次方程组求解挑战
y-9x=13
5x=2y
What is the solution (x, y) to the given system of equations?
原库参考解析
二元一次方程组求解挑战
Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. The second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. What is the cost, in dollars, of 1 dozen eggs?
原库参考解析
二元一次方程组求解基础
The graph of a system of linear equations is shown. The solution to the system is (x, y) .What is the value of x?
原库参考解析
二元一次方程组求解基础
The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution (x, y) to this system?
原库参考解析
二元一次方程组求解基础
y=12x-20
y=28
What is the solution (x, y) to the given system of equations?
原库参考解析
二元一次方程组求解挑战
What system of linear equations is represented by the lines shown?
原库参考解析
二元一次方程组求解挑战
(x-2)-4(y+7)=117
(x-2)+4(y+7)= 442
The solution to the given system of equations is (x, y). What is the value of 6( x- 2)?
原库参考解析
二元一次方程组求解基础
The graph of a system of linear equations is shown. What is the solution (x, y) to the system?
原库参考解析
二元一次方程组求解基础
x = 8
x + 3y = 26
The solution to the given system of equations is (x, y). What is the value of y?
原库参考解析
二元一次方程组求解进阶
\( 3y=4x+17 \)
\( -3y=9x-23 \)
The solution to the given system of equations is \( \left(x,\ y\right) \). What is the value of \( 39x \)?
原库参考解析
二元一次方程组求解基础
\( y=-3x \)
\( 4x+y=15 \)
The solution to the given system of equations is (x, y). What is the value of x?
原库参考解析
