Question

Выясните сколько решение имеет система уравнений {2у=3х-2{1,5х-у=4 Смотреть ответ viktoriyaveklyach viktoriyaveklyach Ответ:3х - 2у = 7; 6х - 4у = 1 - первое уравнение системы домножим на (- 2);- 6x + 4y = - 14; 6x - 4y = 1 - выполним почленное сложение уравнений системы;(- 6x + 6x) + (4y - 4y) = - 14 + 1;0 + 0 = - 13;0 = - 13 - получили не верное равенство, значит данная система уравнений не имеет решений.

Answer 1

Solution to the System of Equations

The given system of equations is:

Equation 1: 2y = 3x - 2 Equation 2: 1.5x - y = 4

To find the solution to this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to solve this system.

Multiplying Equation 1 by -2, we get:

-4y = -6x + 4

Now, let's add this equation to Equation 2:

-4y + 1.5x - y = -6x + 4 + 4

Simplifying the equation, we have:

-5y + 1.5x = -6x + 8

Rearranging the equation, we get:

1.5x + 6x = 5y + 8

Combining like terms, we have:

7.5x = 5y + 8

Now, let's multiply Equation 2 by 2:

3x - 2y = 8

Adding this equation to the previous equation, we have:

7.5x + 3x - 2y = 5y + 8 + 8

Simplifying the equation, we get:

10.5x - 2y = 5y + 16

Rearranging the equation, we have:

10.5x - 5y = 5y + 16

Combining like terms, we have:

10.5x - 10y = 16

Now, let's multiply Equation 2 by 4:

6x - 4y = 16

Adding this equation to the previous equation, we have:

10.5x - 10y + 6x - 4y = 16 + 16

Simplifying the equation, we get:

16.5x - 14y = 32

So, the system of equations can be rewritten as:

16.5x - 14y = 32 10.5x - 10y = 16

Now, let's solve this system of equations.