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挑战
\( x+2y=-8 \)
\( 2x-y=24 \)
The solution to the given system of equations is \( (x,y) \). What is the value of \( x−3y \)?
\( 2x-y=24 \)
The solution to the given system of equations is \( (x,y) \). What is the value of \( x−3y \)?
参考答案
二元一次方程组求解基础
The graphs of two linear equations are shown. A third linear equation is graphed in this xy-plane such that all three lines intersect at exactly one point. Which of the following could be the third linear equation?
I. \( 16x+8y=-7 \)
II. \( -8x+16y=-1 \)
参考答案
二元一次方程组求解基础
\( y=8 \)
\( x=y+9 \)
The solution to the given system of equations is \( (x,y) \). What is the value of x?
\( x=y+9 \)
The solution to the given system of equations is \( (x,y) \). What is the value of x?
参考答案
二元一次方程组求解挑战
\( 6x-2y=5 \)
\( 3x+y=7 \)
The solution to the given system of equations is (x, y). What is the value of \( x+y \)?
\( 3x+y=7 \)
The solution to the given system of equations is (x, y). What is the value of \( x+y \)?
参考答案
二元一次方程组求解挑战
\( x+6y=-2 \)
\( 6x-y=25 \)
The solution to the given system of equations is (x, y). What is the value of \( 5x−7y \)?
\( 6x-y=25 \)
The solution to the given system of equations is (x, y). What is the value of \( 5x−7y \)?
参考答案
二元一次方程组求解基础
\( 6x-2y=5 \)
\( 3x+y=7 \)
The solution to the given system of equations is (x, y). What is the value of \( x+y \)?
\( 3x+y=7 \)
The solution to the given system of equations is (x, y). What is the value of \( x+y \)?
参考答案
二元一次方程组求解基础
\( y=(x+4) \)
\( y=3(x+4)^2 \)
A solution to the given system of equations is (x, y). What is one possible value of x?
\( y=3(x+4)^2 \)
A solution to the given system of equations is (x, y). What is one possible value of x?
参考答案
二元一次方程组求解基础
\( x=4 \)
\( y=7-x \)
The solution to the given system of equations is (x, y). What is the value of y?
\( y=7-x \)
The solution to the given system of equations is (x, y). What is the value of y?
参考答案
二元一次方程组求解进阶
\( -0.9y=0.8x+2.3 \)
\( 4y=-3x+17 \)
The solution to the given system of equations is (x, y). What is the value of x?
\( 4y=-3x+17 \)
The solution to the given system of equations is (x, y). What is the value of x?
参考答案
二元一次方程组求解挑战
\( y=(x-2)(x+7) \)
\( y=9x-18 \)
Which ordered pair (x, y) is the solution to the given system of equations?
\( y=9x-18 \)
Which ordered pair (x, y) is the solution to the given system of equations?
参考答案
二元一次方程组求解基础
\( x=5 \)
\( y=7-x \)
The solution to the given system of equations is (x, y). What is the value of y?
\( y=7-x \)
The solution to the given system of equations is (x, y). What is the value of y?
参考答案
二元一次方程组求解挑战
\( \frac{x-13}{6}+\frac{y+26}{3}=-5 \)
\( \frac{x-13}{3}-\frac{y+26}{6}=5 \)
The solution to the given system of equations is (x, y). What is the value of \( x−y \)?
\( \frac{x-13}{3}-\frac{y+26}{6}=5 \)
The solution to the given system of equations is (x, y). What is the value of \( x−y \)?
参考答案
