Solve x-3t=6 and 4x+3t=9

well, we know that x = 3t+6, so use it:

4(3t+6)+3t = 9
12t+24+3t = 9
15t = -15
t = -1
so, x = 3t+6 = 3

To solve the system of equations:

1. Start by eliminating one variable. In this case, we'll eliminate t.
Multiply the first equation by 3:
3(x - 3t) = 3(6) or 3x - 9t = 18

2. Next, add the two equations together to eliminate t:
(3x - 9t) + (4x + 3t) = 18 + 9
Combine like terms: 7x - 6t = 27

3. Now you have a new equation with just one variable.
Solve this equation for x:
7x - 6t = 27
7x = 27 + 6t
Divide both sides by 7:
x = (27 + 6t) / 7

4. Substitute this value of x into one of the original equations to solve for t. Let's use the first equation:
x - 3t = 6
Substitute x with (27 + 6t) / 7:
((27 + 6t) / 7) - 3t = 6

5. Solve for t:
Simplify the equation:
(27 + 6t) - 21t = 42
Combine like terms:
27 - 15t = 42
Subtract 27 from both sides:
-15t = 15
Divide both sides by -15:
t = -1

6. Substitute t = -1 into the value of x from step 3 to find x:
x = (27 + 6(-1)) / 7
Simplify:
x = (27 - 6) / 7
x = 21 / 7
x = 3

Therefore, the solution to the system of equations is x = 3 and t = -1.