Solve this system by substitution

2x-3y=12
x-4y=6

x = 6 + 4y

Substitute x-value into the other equation.

2(6 + 4y) - 3y = 12

Solve for y and put that value into the top equation to find x.

I hope this helps. Thanks for asking.

To solve this system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation. Let's begin:

Step 1: Solve one equation for one variable.
Let's solve the second equation (x-4y=6) for x:
x = 6 + 4y

Step 2: Substitute the expression for the variable into the other equation.
Now we will substitute the expression we got for x (6 + 4y) into the first equation (2x - 3y = 12):
2(6 + 4y) - 3y = 12

Step 3: Simplify and solve.
Distribute 2 to the terms inside the parentheses:
12 + 8y - 3y = 12

Combine like terms:
5y = 12 - 12
5y = 0

Divide both sides of the equation by 5:
y = 0/5
y = 0

Step 4: Find the value of the other variable.
Now that we have found y, we can substitute it back into one of the original equations to solve for x.
Let's use the second equation (x-4y=6):
x - 4(0) = 6
x - 0 = 6
x = 6

Step 5: Check your solution.
To check if the solution is correct, substitute the values of x and y back into the original equations and see if they satisfy both equations.

In this case, when we substitute x = 6 and y = 0 into both equations:
Equation 1: 2x - 3y = 12
2(6) - 3(0) = 12
12 - 0 = 12, which is true.

Equation 2: x - 4y = 6
6 - 4(0) = 6
6 - 0 = 6, which is also true.

Therefore, the solution to the system of equations is x = 6 and y = 0.