Question

Розв'яжіть систему рівнянь x+3/2-y-2/3=2 x-1/4+y+1/3=4 пожалуйста очень срочно!

Answer 1

відповідь на фотографії.

Answer 2

Solving the System of Equations

To solve the system of equations:

x + 3/2 - y - 2/3 = 2
x - 1/4 + y + 1/3 = 4

we can use the method of elimination or substitution. Let's solve it using the method of elimination.

Method of Elimination

To eliminate one variable, we can multiply the first equation by 4 and the second equation by 6 to get rid of the fractions:

4(x + 3/2 - y - 2/3) = 4(2)
6(x - 1/4 + y + 1/3) = 6(4)

Simplifying these equations, we have:

4x + 6 - 8y - 8/3 = 8
6x - 3/2 + 6y + 2 = 24

Now, let's rearrange the equations:

4x - 8y = 8 - 6 + 8/3
6x + 6y = 24 + 3/2 - 2

Simplifying further:

4x - 8y = 10/3
6x + 6y = 25/2

Solving the Simplified System

Now we have a simplified system of equations:

4x - 8y = 10/3
6x + 6y = 25/2

We can solve this system using the method of elimination or substitution. Let's use the method of elimination again.

Multiplying the first equation by 3 and the second equation by 2, we get:

3(4x - 8y) = 3(10/3)
2(6x + 6y) = 2(25/2)

Simplifying these equations, we have:

12x - 24y = 10
12x + 12y = 25

Now, let's subtract the second equation from the first equation:

(12x - 24y) - (12x + 12y) = 10 - 25

Simplifying further:

12x - 24y - 12x - 12y = -15
-36y = -15

Dividing both sides of the equation by -36, we get:

y = -15 / -36

Simplifying:

y = 5 / 12

Now, let's substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:

x + 3/2 - (5/12) - 2/3 = 2

Simplifying this equation, we have:

x + 3/2 - 5/12 - 2/3 = 2

Combining the fractions:

x + 18/12 - 5/12 - 8/12 = 2

Simplifying further:

x + 5/12 = 2

Subtracting 5/12 from both sides of the equation:

x = 2 - 5/12

Simplifying:

x = 24/12 - 5/12

Combining the fractions:

x = 19/12

Solution

Therefore, the solution to the system of equations is:

x = 19/12
y = 5/12

Please note that the solution has been calculated based on the given equations.