Question

2 системы алгебра с решением

Answer 1

1   х²-5ху=6        х(х-5у)=6
     х-5у=1            х*1=6             х=6    у=1
 
 
 2     2х+у=4          2х+3х=6+4
        3х-у=6           5х=10            х=2    у=0

Answer 2

Two Algebraic Systems with Solutions

There are many algebraic systems with solutions, so it would be helpful if you could provide more specific information about the systems you are referring to. However, I can provide some general information about algebraic systems and their solutions.

An algebraic system typically consists of a set of equations or inequalities that need to be solved simultaneously. The solutions to the system are the values of the variables that satisfy all the equations or inequalities.

Here are two examples of algebraic systems with their solutions:

Example 1: Consider the following system of equations: 1) x + y = 4 2) y + yx = 6

To find the solution to this system, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the substitution method:

From equation 1, we can express x in terms of y as x = 4 - y. Substituting this value of x into equation 2, we get: (4 - y) + y(4 - y) = 6

Simplifying the equation, we have: 4 - y + 4y - y^2 = 6 -y^2 + 3y - 2 = 0

Factoring the quadratic equation, we get: -(y - 2)(y - 1) = 0

This equation has two solutions: y = 2 and y = 1. Substituting these values back into equation 1, we can find the corresponding values of x: For y = 2, x = 4 - 2 = 2 For y = 1, x = 4 - 1 = 3

Therefore, the solution to the system of equations is x = 2, y = 2 and x = 3, y = 1.

Example 2: Consider the following system of equations: 1) 8x + 2y = 46 2) 7x + 3y = 47

To solve this system, we can use the elimination method. Multiplying equation 1 by 3 and equation 2 by 2, we can eliminate the y variable: 3(8x + 2y) = 3(46) -> 24x + 6y = 138 2(7x + 3y) = 2(47) -> 14x + 6y = 94

Subtracting the second equation from the first equation, we get: (24x + 6y) - (14x + 6y) = 138 - 94 10x = 44 x = 4.4

Substituting the value of x into equation 1, we can find the value of y: 8(4.4) + 2y = 46 35.2 + 2y = 46 2y = 10.8 y = 5.4

Therefore, the solution to the system of equations is x = 4.4, y = 5.4.

Please note that these are just two examples of algebraic systems with solutions. There are many other types of systems and methods to solve them. If you have a specific system in mind, please provide more details so that I can assist you further.