How to solve the equation with two variables

How to solve the equation with two variables

Sometimes at the solution of the simple equations with two unknown many school students have small difficulties. However you should not despair! It is a little efforts, and you will be able to solve any equations.


1. Let's say you have an equation: the 2nd + at =10kh-at =2reshit it it is possible in several ways.

2. A way you podstanovkivyrazit one variable and substitute it in other equation. It is possible to express any variable at your discretion. For example, express "at from the second equation: x - at =2 => at = x-2Zatem substitute everything in the first equation: + (x-2) =10perenesite all numbers without "x in the right part also count the 2nd: the 2nd + x =10+23kh =12 Further to find "x, divide both members of equation into 3: x =4. So, you found "x. Find "at. For this purpose substitute "x in that equation from which you expressed "at: at = x-2=4-2=2u =2.

3. Make check. For this purpose substitute the turned-out values in the equations: 2*4+2=104-2=2neizvestny are found truly!

4. Way of addition or subtraction uravneniyizbavtes at once from some changed. In our case it is simpler to make it with "at. As in the first equation "at with the sign "+, and in the second "-, you can execute addition operation, i.e. we put the left part with left, and right from right: the 2nd + at + (x - s) =10+2preobrazuyte: + at + x - at =10+23kh the =12th =4podstavte "x in any equation also find the 2nd "at: 2*4+ at =108+ at =10u =2po to the 1st way you can check a =10-8a that roots are found truly.

5. If there are no accurately expressed variables, then it is necessary to transform the equations a few. In the first equation we have "the 2nd, and in the second it is simple "x. In order that at addition or subtraction "x it was reduced, increase the second equation by 2: x - at a =22kh-2a =4zatem subtract the second from the first equation: the 2nd + at - (2kh-2) =10-4zamety if the bracket is faced by minus, then after disclosure change signs for opposite: + at-2h +2u =63u =6u =2 "x find the 2nd, having expressed from any equation, i.e. x =4

Author: «MirrorInfo» Dream Team