Advice 1: How to solve an equation with two variables

Sometimes when solving simple equations with two unknowns, many students have a little difficulty. However, do not despair! A little effort and you will be able to solve any equation.
How to solve an equation with two variables
Instruction
1
Let's say you have the equation:
2x+y=10
x-y=2
It can be solved in several ways.
2
Way to postuniversity one variable and substitute it into another equation. It is possible to Express any variable of your choice. For example, Express "from the second equation:
x-y=2 => y=x-2Затем all the substitute in the first equation:
2+(x-2)=10Перенесите all the numbers without "x to the right side and calculate:
2x+x=10+2
3=12 Then, to find x , divide both sides of equation by 3:
x=4.So, you have found "x . Find ". To do this, substitute the "x in the equation from where you have expressed ":
y=x-2=4-2=2
y=2.
3
Make the check. To do this, substitute the resulting values into the equations:
2*4+2=10
4-2=2
Unknown found right!
4
Method of addition or subtraction uraninites from some variable. In our case it is easier to do with ".
As in the first equation "the sign", and the second " - then you can perform the operation of addition, i.e. the left part of the fold on the left and the right on the right:
2x+y+(x-y)=10+2Преобразуйте:
2x+y+x-y=10+2
3=12
x=4Подставьте "x in any equation and find ":
2*4+y=10
8+y=10
at=10-8
y=2 on the 1st way you can check that the roots are found true.
5
If there is no clearly defined variables, it is necessary to convert the equation.
In the first equation have a "2 , and the second just "x . To the addition or subtraction of "x was reduced, multiply the second equation by 2:
x-y=2
2-2U=4Затем subtract the first equation from the second:
2x+y-(2x-2Y)=10-4Заметим, if before the parenthesis is minus, then after the disclosure adjust the marks to the opposite:
2x+y-2x+2Y=6
3y=6
y=2"x, find the expressing of any equation, i.e.,
x=4

Advice 2: How to solve linear equation with two variables

The equation, in General written ax+by+C=0, is called a linear equation with two variables. This equation in itself contains an infinite number of solutions, so the task it is always complemented by either another equation or bounding condition. Depending on conditions, will be given a task, solve a linear equation with two variables follows different ways.
How to solve linear equation with two variables
You will need
  • - linear equation with two variables;
  • - the second equation or additional terms.
Instruction
1
If given a system of two linear equations, solve it in the following way. Select one of the equations in which the coefficients in front of variables is smaller and Express one of the variables, e.g., x. Then substitute this value contains, in the second equation. In the resulting equation will have only one variable y, move all the parts from the left side, and the free members to the right. Find and replace any of the original equations to find X.
2
To solve a system of two equations in another way. Multiply one of the equations on a number below the coefficient in front of one of the variables, for example, before x was the same in both equations. Then subtract one equation from the other (if the right side is not equal to 0, don't forget to deduct the same and right parts). You will see that the variable x disappeared, leaving only one variable. Solve the resulting equation, and substitute the value found in any of the original equations. Find H.
3
The third method of solving systems of two linear equations – graphical. Draw a coordinate system and draw the graphs of two straight lines whose equations are provided in your system. For this, substitute any two values of x in the equation and find the corresponding y – it will be the coordinates of the points belonging to a straight line. It is most convenient to find the intersection with the coordinate axes is sufficient to substitute the values x=0 and y=0. The coordinates of the point of intersection of these two lines will be the solution of the problem.
4
If the conditions of the problem, only one linear equation, so you are given additional conditions that can help you find a solution. Carefully read the task to find these terms. If variables x and y denoted the distance, speed, age, and weight – feel free to put the constraint x≥0 and y≥0. It is possible, under x or hides the number of children, apples, trees, etc. – then values can only be integers. If x is the age of the son, it is clear that he can't be older than my father, so specify it in terms of the problem.
5
Plot the straight line, the corresponding linear equation. Look at the chart, perhaps it will be only a few solutions satisfying all conditions – for example, integers and positive integers. They will be solutions of your equation.
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