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.