Question

Упростить и решить рациональным способом систему линейных уравнений: {3x-2(x+y)=13 {4(x-y)-3x=19

Answer 1

3х-2(х+у)=13

4(х-у)-3х=19

 

3х-2х-2у=13

4х-4у-3х=19

 

х-2у=13

х-4у=19

 

х=13+2у

13+2у-4у=19

 

-2у=6

у=-3

х=13-6=7

 

Ответ: х=7; у=-3

 

 

Answer 2

3x-2(x+y)=13

4(x-y)-3x=19

3X-2X-2Y=13

4x-4y-3x=19

x-2y=13

x-4y=19

x=13+2y

13+2y-4y=19

13-2y=19

-2y=6

y=-3

x=7

Answer 3

Simplifying and Solving the System of Linear Equations

To simplify and solve the system of linear equations: 3x - 2(x + y) = 13 4(x - y) - 3x = 19

We can start by simplifying the equations and then solving for the variables.

First, let's simplify the equations: 1. 3x - 2(x + y) = 13 2. 4(x - y) - 3x = 19

To simplify the first equation, we distribute the -2: 1. 3x - 2x - 2y = 13 2. x - 2y = 13

Now, let's simplify the second equation: 1. 4x - 4y - 3x = 19 2. x - 4y = 19

Now we have the simplified system of equations: 1. x - 2y = 13 2. x - 4y = 19

Next, we can solve the system of equations using the substitution method. Subtracting the first equation from the second gives us: 1. x - 2y = 13 2. -2y = 6

Solving for y: y = -3

Substituting y back into the first equation: x - 2(-3) = 13 x + 6 = 13 x = 7

So, the solution to the system of linear equations is: x = 7 y = -3

This is the simplified and solved system of linear equations.