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What is the difference between the form of the equation of first degree with one variable and that of first degree with two variables Differences in writing form
One variable linear equation, there is only one unknown x, the figure drawn is a point on one-dimensional straight line. Example: x + 4 = 6, so x = 2. X is a point, the value is 2. Two variable linear equation, there are two unknown x, y, the figure drawn is a line on two-dimensional plane. Example: x + y = 3, when x = 0, y = 3, when y = 0, x = 3
The concept of solutions of linear equation with one variable and the concept of solutions of linear equation with two variables
Linear equation of one variable: an integral equation with only one unknown number (i.e. "element") and the highest degree of the unknown number is 1 (i.e. "degree"). The value of the unknown number which makes the left and right sides of the equation equal is called the solution of the equation
To solve and explain the linear equation of one variable, the linear equation of two variables,
What is a linear equation of one variable, a linear equation of two variables, a linear equation of three variables? Can you give me an example to explain each one?
"Yuan" stands for the unknown, and "times" stands for the highest number of unknowns
Linear equation of one variable: an equation with one unknown and the highest degree of the unknown is one
For example: x + 3 = 0
Bivariate linear equation: an equation with two unknowns and the highest degree of unknowns is 1
For example: x + 2Y + 3 = 0
Trivariate linear equation: an equation with three unknowns and the highest degree of unknowns is 1
For example: x + 3Y + 4Z + 13 = 0
Take another example
Quadratic equation of one variable: an equation with one unknown and the highest degree of the unknown is 2
For example: X & # 178; + X + 3 = 0
May I ask you math experts, binary linear equation will be more difficult to understand than unary linear equation?
I'm a junior high school student. I'm not very good at mathematics. Recently I'm learning binary linear equation. In fact, I didn't learn it very well last semester. But after several classes, I think binary linear equation is much simpler than unitary linear equation. Why? The old teacher said that binary linear equation is based on unitary linear equation. If you can't learn it well, you can't learn binary linear equation well, But I don't think so. These homework books are all right. Am I really a miracle?
Can a linear equation of one variable and a linear equation of two variables form a system of linear equations of two variables
Yes, you can take the equation of one variable once as the second variable of one variable once only, that is, the coefficient in front of Y is 0!
The solution of a bivariate linear equation and a bivariate linear equation system is x = 2, y = - 4. Try to write a satisfactory equation system
One is enough
x-y=6
2x=4
It is known that the solutions of a system of linear equations of two variables composed of a linear equation of two variables and a linear equation of one variable are x = 1, y = 2 and x = - 1, y = - 2
Find such a system of equations
The solution is x = 1, y = 2
X + y = 3 and x = 1
The equations with solutions x = - 1 and y = - 2 are
X + y = - 3 and x = - 1
Veda's theorem for quadratic equation of one variable
It is known that the equations X & # 178; - (P-3) x + 5p-3 = 0 and X & # 178; - 4x-m = 0 have a common root, and the sum of two non-common roots is obtained
Let the common root be X. - (P-3) x + 5p-3 = - 4x-m. so x = (5p-3 + m) / (p-7). 2x = 2 (5p-3 + m) / (p-7)
Let the first two equations be x, x1, then x + X1 = (P-3) / 2
Let the second equation be x, X2, then x + x2 = 2
X1 + x2 + 2x = (P + 1) / 2, so X1 + x2 = (P + 1) / 2-2 (5p-3 + m) / (p-7)
Veda's theorem for quadratic equation of one variable
Given that a and B satisfy a & # 178; - 15a-5 = 0, B & # 178; - 15b-5 = 0, find a / B + B / A
The answer given at the end of the book is - 47 When a ≠ B, and 2 when a = B
My question is, is the answer correct? If it's correct, why should we classify? In addition, if we need to classify, there are discussions on the Internet about a = - B, which is too annoying. I just don't understand the reason for classification discussion
The solution by Weida theorem: if two of the quadratic equation 2x ^ 2-6x + 3 = 0 are a and B, find the value of (a-b) ^ 2
From Veda's theorem, it is concluded that
a+b=3,ab=3/2
∴(a-b)²
=(a+b)²－4ab
=3²－4×(3/2)
=9－6
=3
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