pls help me to solved this equation

1. 6y=x+18
2y-x=6,
2. 4x=3y=13
2x-4y=1
3. y=3x-12
2/3x=2/3-1/6y pls help me now. this equation is Systems of Linear Equations Solved Algebraically.

1. x=18-6y

2y-6=x

therefore, 18-6y = 2y-6
18+6=2y+6y
24=8y
y=3

x= 18-6y
18-(6x3)
x=0

Do the rest by your own.

To solve a system of linear equations algebraically, you can use different methods such as substitution, elimination, or matrix methods. Let's solve each system one by one:

1. System of Equations:
Equation 1: 6y = x + 18 ---(1)
Equation 2: 2y - x = 6 ---(2)

We can solve this system using the method of substitution.
First, solve equation (1) for x:
x = 6y - 18

Substitute this value of x into equation (2):
2y - (6y - 18) = 6
2y - 6y + 18 = 6
-4y = -12
y = 3

Now substitute the value of y into equation (1):
6(3) = x + 18
18 = x + 18
x = 0

Therefore, the solution to this system of equations is x = 0 and y = 3.

2. System of Equations:
Equation 1: 4x + 3y = 13 ---(1)
Equation 2: 2x - 4y = 1 ---(2)

This system can be solved using the method of elimination.
Multiply equation (1) by 2 and multiply equation (2) by 4 to eliminate the x variable:
Equation 1: 8x + 6y = 26
Equation 2: 8x - 16y = 4

Subtract equation (2) from equation (1) to eliminate x:
(8x + 6y) - (8x - 16y) = 26 - 4
22y = 22
y = 1

Substitute the value of y into equation (1):
4x + 3(1) = 13
4x + 3 = 13
4x = 10
x = 2.5

Hence, the solution to this system of equations is x = 2.5 and y = 1.

3. System of Equations:
Equation 1: y = 3x - 12 ---(1)
Equation 2: (2/3)x = (2/3) - (1/6)y ---(2)

This system can be solved by substituting the value of y from equation (1) into equation (2).

Substitute the value of y from equation (1) into equation (2):
(2/3)x = (2/3) - (1/6)(3x - 12)
(2/3)x = (2/3) - (1/6)(3x) + (1/6)(12)
(2/3)x = (2/3) - (1/2)x + 2
Multiply through by 6 to get rid of fractions:
4x = 4 - 3x + 12
4x + 3x = 4 + 12
7x = 16
x = 16/7

Now substitute the value of x into equation (1):
y = 3(16/7) - 12
y = 48/7 - 84/7
y = -36/7

Therefore, the solution to this system of equations is x = 16/7 and y = -36/7.

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