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进阶
mx+ky=-83
2x+ky=22
In the given system of equations, m and k are constants. The graphs of these equations in the xy-plane intersect at the point (5, y). What is the value of m?
原库参考解析
二元一次方程组求解挑战
(x-3)-8(y+9)=129(x-3)+8(y+9)=432The solution to the given system of equations is (x, y). What is the value of 8(x-3)?
原库参考解析
二元一次方程组求解挑战
y=5(x-2)2
y=10(x-2)
A solution to the given system of equations is (x, y). What is one possible value of x+y?
原库参考解析
二元一次方程组求解进阶
mx+ ky = -83
2x + ky = 22
In the given system of equation, m and k are constants. The graphs of these equations in the xy-plane intersect at the point (5, y). What is the value of m ?
原库参考解析
二元一次方程组求解挑战
(x - 3) - 8(y + 9) = 129
(x - 3) + 8(y + 9) = 432
The solution to the given system of equations is (x, y). What is the value of 8(x - 3) ?
原库参考解析
二元一次方程组求解挑战
y =5(x -2)2
y =10(x -2)
A solution to the given system of equations is (x, y). What is one possible value of x + y ?
原库参考解析
二元一次方程组求解进阶
5x ＋5y = 150
x＋y =2x
lf the solution to the given system of equations is(x, y), which of the following equations is true?
原库参考解析
二元一次方程组求解进阶
\( 2y=8x+19 \)
\( -2y=9x-28 \)
The solution to the given system of equations is (x , y). What is the value of 68x?
原库参考解析
二元一次方程组求解挑战
\( 20x+19y= c \)
\( 19x-20y=c \)
In the given system of equations, c is a positive constant. Which of the following could be the point where the graphs of the equations in this system intersect in the xy-plane?
原库参考解析
二元一次方程组求解进阶
\( x+33=y \)
\( \left(x+33\right)^2=y \)
A solution to the given system of equations is (x, y). What is a possible value of x?
原库参考解析
二元一次方程组求解挑战
\( -x-wy=-337 \)
\( 2x-wy=47 \)
In the given system of equations, w is a constant. In the xy-plane, the graphs of these equations intersect at the point (q, 19), where q is a constant. What is the value of w?
原库参考解析
二元一次方程组求解挑战
\( y=3x+9 \)
\( 3y=8x-6 \)
The solution to the given system of equations is (x, y). What is the value of \( x−y \) ?
原库参考解析
