Question

Решите систему уравнений! {10-(9x-2y)=18-4y} {2x-3(1+y)=2(3x-y)} любым способом!!

Answer 1

10-(9x-2y)=18-4y

2x-3(1+y)=2(3x-y)

 

2x-3(1+y)=2(3x-y)

2x-3-3y-6x+2y=0

-4x-3-y=0

y=-4x-3

 

10-(9x-2y)=18-4y

10-9x+2y-18+4y=0

-8-9x+6y=0

-8-9x+6*(-4x-3)=0

-8-9x-24x-18=0

-26-33x=0

x=-26/33

 

-4*(-26/33)-3-y=0

104/33-3-y=0

y=5/33

Answer 2

Solving the System of Equations

To solve the system of equations:

{10-(9x-2y)=18-4y} {2x-3(1+y)=2(3x-y)}

We can use the given equations to find the values of x and y.

Let's solve the system step by step:

Step 1: Simplify the Equations

Simplifying the first equation: 10 - (9x - 2y) = 18 - 4y 10 - 9x + 2y = 18 - 4y -9x + 2y + 4y = 18 - 10 -9x + 6y = 8

Simplifying the second equation: 2x - 3(1 + y) = 2(3x - y) 2x - 3 - 3y = 6x - 2y 2x - 6x = 2y - 3y + 2 -4x = -y - 2

Step 2: Rearrange the Equations

Rearranging the first equation: -9x + 6y = 8 -9x = 8 - 6y x = (8 - 6y) / -9

Rearranging the second equation: -4x = -y - 2 x = (-y - 2) / -4

Step 3: Equate the Expressions for x

Setting the expressions for x equal to each other: (8 - 6y) / -9 = (-y - 2) / -4

Step 4: Solve for y

Cross-multiplying and simplifying: -4(8 - 6y) = -9(-y - 2) -32 + 24y = 9y + 18 24y - 9y = 18 + 32 15y = 50 y = 50 / 15 y = 10/3

Step 5: Substitute y into one of the Equations

Substituting y = 10/3 into the first equation: -9x + 6(10/3) = 8 -9x + 20 = 8 -9x = 8 - 20 -9x = -12 x = -12 / -9 x = 4/3

Step 6: Solution

The solution to the system of equations is x = 4/3 and y = 10/3.

Therefore, the solution to the given system of equations is x = 4/3 and y = 10/3.