Answer:
The system of linear equations has no solution.
Explanation:
We can solve the system of linear equations using substitution or elimination method.
Here's how you can solve it using substitution:
Solve one equation for either x or y.
Substitute the expression you found in step 1 into the other equation.
Solve for the remaining variable.
Use the values you found in steps 3 to find the other variable.
Starting with the first equation:
3y = 6 + x
Solving for x:
x = 3y - 6
Next, we substitute this expression into the second equation:
3x - 9y = 9
Plugging in x = 3y - 6:
3(3y - 6) - 9y = 9
Expanding the left-hand side:
9y - 18 - 9y = 9
Combining like terms:
0y - 18 = 9
Adding 18 to both sides:
0y = 27
Since y cannot equal 0, we have a contradiction and the system has no solution.
So, the system of linear equations has no solution.