Question

система уравнений

Answer 1

(2х–3у)(2х+3у)=12 2х–3у=3; 3(2х+3у)=12 2х–3у=3; 2х+3у=4 2х–3у=3; 2х=4–3у (4–3у)–3у=3; 2х=4–3у 4–6у=3; 2х=4–3у 6у=1; 2х=4–3у у=1/6; 2х=4–3*1/6 у=1/6; 2х== 4–1/2 у =1/6; 2х=7/2 у=1/6; х =7/4 у =1/6.

Answer 2

{4x^2  -  9y^2  =  12      {(2x  -  3y)(2x  +  3y)  =  12    3(2x  +  3y)  =  12  2x + 3y = 4
{2x  -  3y  =  3

{2x  +  3y  =  4    Решим  систему  методом  сложения
{2x  -  3y  =  3
4х  =  7       х  =  7/4       х  =  1,75
2*1,75  +  3у  =  4         3у  =  4  -  1,5    3у  =  2,5    у  =  2,5/3      у  =  5/6
Ответ.          (1,75;     5/6)   

Answer 3

System of Equations

A system of equations is a set of equations that are solved simultaneously to find the values of the variables that satisfy all the equations in the system. There can be different methods to solve a system of equations, such as substitution, elimination, or using matrices.

Let's look at some examples of systems of equations and their solutions:

1. Example 1: 3x + 2y = 8 and 2x + 6y = 10 To solve this system, we can use the method of elimination or substitution. Let's use the elimination method: - Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations the same: - 9x + 6y = 24 - 4x + 12y = 20 - Subtract the second equation from the first equation: - (9x + 6y) - (4x + 12y) = 24 - 20 - 5x - 6y = 4 - Now we have a new equation: 5x - 6y = 4. We can solve this equation along with one of the original equations to find the values of x and y.

2. Example 2: 2x + 3y = 8 and 4x - 2y = 10 To solve this system, we can use the method of substitution: - Solve one equation for one variable and substitute it into the other equation: - From the first equation, we can solve for x: x = (8 - 3y) / 2 - Substitute this value of x into the second equation: 4((8 - 3y) / 2) - 2y = 10 - Simplify and solve for y: - (16 - 6y) - 2y = 10 - 16 - 6y - 2y = 10 - 16 - 8y = 10 - -8y = 10 - 16 - -8y = -6 - y = -6 / -8 - y = 3/4 - Substitute the value of y back into the first equation to find x: - 2x + 3(3/4) = 8 - 2x + 9/4 = 8 - 2x = 8 - 9/4 - 2x = 32/4 - 9/4 - 2x = 23/4 - x = 23/4 * 1/2 - x = 23/8

These are just a couple of examples of solving systems of equations. There are different methods and techniques that can be used depending on the specific equations in the system.

I hope this helps! Let me know if you have any further questions.