Substitution

X-6y=4
3x-18y=4

X-6y=4

3x-18y=4

x = 6y + 4

3(6y + 4) = 18y + 4
18y + 12 = 18y + 4

Can't be solved

To solve this system of equations using substitution, follow these steps:

1. Solve one of the equations for one of the variables.
Let's take the first equation, X-6y=4. Solving for X, we get:
X=4+6y

2. Substitute the expression for the variable found in step 1 into the other equation.
Substitute X=4+6y into the second equation, 3x-18y=4:
3(4+6y)-18y=4

3. Solve the resulting equation for the remaining variable.
Distribute the 3 into the parentheses: 12+18y-18y=4
Simplify the equation: 12=4

4. Analyze the result.
The equation 12=4 is a contradiction. It means that the two original equations do not have a common solution. Therefore, this system of equations is inconsistent, and there is no solution.

In conclusion, the system of equations X-6y=4 and 3x-18y=4 is inconsistent, meaning there is no solution that satisfies both equations simultaneously.